There's the briefest of pauses before David Haye proclaims, "That's a gigabyte every 20 seconds." Our photographer has asked him to bear with him while his laptop processes the enormous images his quickfire shooting is forcing it to deal with. Earlier on, Haye told me he "was never good at maths".

As innocuous a moment as it may seem, it's symbolic: three hours with David Haye is enough to hammer home the point that, beyond the bluster, the showmanship, the occasional fight at a press conference, is one of the sharpest minds in the sport of boxing.

Whatever your thoughts on 'The Hayemaker' – he's been a polarising character pretty much since day one – no one could deny that now is a particularly interesting time to talk to him. Off the back of a few years out of the ring through injury, he's now on the comeback trail. In his first fight in almost three and a half years, he saw off Mark de Mori inside the first round at a packed O2 Arena, and he's looking to do the same on 21 May when he takes on Arnold Gjergjaj at the same venue. Now, he has his sights set not just on winning back the title of heavyweight champion of the world, but of unifying the belts in that weight class, eight years after he achieved the same feat in the cruiserweight division with a breathtaking flurry of punches to knock out Enzo Maccarinelli.

Haye admits he feels more comfortable at heavyweight than cruiserweight, and even in an immaculately tailored Timothy Everest suit, he looks the part. But despite that, and despite repeatedly claiming he'd retire at 30, the fact that he didn't unify those heavyweight titles has weighed on his mind since his loss to Wladimir Klitschko in 2013, when he was carrying a foot injury that affected his explosive power and dulled his performance. He's a born winner and has grown to hate losing: "I have no time for losing well – I'd rather win horribly. If I lose I hate it and I'll do anything I can to avoid that ever happening again. I've only lost twice as a professional, but that's two times too many for me."

I've only lost twice as a professional, but that's two times too many

When I ask him if he'd have come back to the sport if he'd ended up unifying both divisions, he's unequivocal: "No, I wouldn't have done. That was my goal, and I failed on that count. I tried to unify them, lost the fight on points and it didn't go how I anticipated. I didn't envisage losing before I retired, and I did; I lost the fight on points. It was very frustrating, but I said I'd retire before I was 31, I nearly did that, but it didn't quite happen. It wasn't meant to be. Now here I am five years on, fighting these younger, fresher guys.

"When your opponent brings a belt with him, that's always good, because you know you're going into the record books. You might not go into record books for fighting a big-name fighter because you don't know how he'll be remembered in time, but the record books would state you were the champion of a respected governing body on this day. In 100 years' time, who was the WBA champion of the world in 2009? That was David Haye. 2010? David Haye. 2011? David Haye. 2012, it wasn't me – so in 2016 I'd love to be a two-time heavyweight champion of the world."

Heavy Hitters

The Hayemaker on a potential match-up with previous Square mile cover star Anthony Joshua

Of all the heavyweights out there, there's one in particular Haye's got his eye on: "Anthony Joshua now is fighting for a world title, quite rightly, as he's had a punch-perfect career. When he was a young guy coming through, I was giving him as much advice as I could. I never really saw him as a potential opponent back then, but the reality is he's the next biggest thing out there. So, if people believe he's the best in the world, and he can prove that in his next fight, then that's what I want."

By the time you're reading this, Joshua will have fought Charles Martin (also at the O2). If, as expected, Joshua has won that – and Haye wins his own Haye Day fight on 21 May against Arnold Gjergjaj – the likelihood is the two will pair up for a world championship bout. "At cruiserweight, I tussled with Enzo Maccarinelli. When he was a cruiserweight champion and I was the cruiserweight champion; we unified the belts. I'd love that; I'd love a unification fight with Joshua. Even if it's not a unification fight, I will challenge him for his belt."

"In the time that I've been out injured, Anthony Joshua has won the Olympics and had his whole professional career. That's how long three-and-a-half years means in professional boxing. I've got a little bit of lost time to make up.

"I was the world heavyweight champion after being the first unified cruiserweight champion ever. I achieved all of that and became the heavyweight champion before Anthony Joshua (age 26) even started boxing. So when it comes to experience, I don't think it's close in any way, shape or form – I believe I've forgotten more about boxing than he currently knows. That doesn't mean I will automatically win, it means I've been around boxing a lot more, and I think when we fight, I believe that will play a big part in it. Obviously he's younger; he's bigger, stronger, fresher – I just don't believe he has the technical know-how to be able to shut me down. 

"It's all good saying that, but you've got to get in the ring and prove it. Some people who have followed me throughout my career would back me; some of the new kids on the block now who may not have seen me fight – who might have become fans of boxing because of Joshua winning at the Olympics – might have got on the bandwagon and think I'm an old boxer coming out of retirement. So, it's split down the middle, and that's when you really do get exciting times in boxing, when the public are split."

For any boxing fan, it's a mouthwatering prospect. As Haye says, "British boxing wins either way. Whoever wins that fight, the British public have seen two of the best going at it."

Cover by David Harrison

Some boxers love to talk, and Haye is clearly one of them. But he – at least the 2016 version – is a man who has a clear, precise vision of how the sport operates, and of his position within it. And, refreshingly, he's effusive about the fuel that drives boxing: money. "If you fight every six months or so at world level and you're not telling anyone you're fighting, you're not vocal about what you do, then no one is going to see you, no one is going to pay for you and you're not going to make any money. And you're not going to get looked after by the television networks and governing bodies. So you need to be vocal about who you are and what you believe in and who you believe you can beat."

Haye has been outspoken against upcoming opponents in the past, and been embroiled in his share of pre-fight controversy, but he insists it's part and parcel: "It's just a sport," he says. "There's not one person on the planet that I hate. Even when I was fighting Dereck Chisora and he drew me into having a punch-up at a press conference with him, I had all rights to hate him; but I never did. I wasn't a fan of his but I respected him as an athlete – I respected his skill set, his strength, his toughness, durability. If I didn't respect those things I might have lost that fight. I had to go out there and put on a masterclass – to push my body to the limit in training, so come fight night things would be easy. And they were easy; I predicted a fifth-round knockout and that's exactly what I got in that fight."

I ask him whether boxers can be too vocal – and whether the sport's and the fighters' profiles afford too much limelight. In particular, I ask about Tyson Fury's recent, ill-judged comments about some controversial subjects that had nothing to do with the sport. "If he [Fury] gets paid a lot of money, then can you argue with him?" Haye asks, sceptically. "But if he's not getting paid much, which I don't think he is – from what I heard what he got paid for the Klitschko fight and what he's getting paid for the rematch isn't a lot of money – getting the amount of criticism he got, saying the things about comparing homosexuals to paedophiles and all this crazy stuff, I don't think it was worth it.

"If he was getting paid £10m and he said that, you'd think 'Did he really mean it or was he just saying it for the money?' But he's not really getting any money – so why did he say it? He's young – he's in his 20s – as he gets older he'll probably look back and cringe.

"I always hammed it up a lot more when I was younger," Haye admits. "I used to just say controversial things that I knew would get headlines because, even though they were negative, a headline is a headline. But it gets people interested, and the more people are interested, the more people buy the fight; the more people buy the fight, the more money I get paid. But I had to get used to what people want, and the hype. How far can you push it before it becomes 'that's way too much, David, you've got to rein this in'?

"You then lose your endorsements and then you start losing money. It's one thing saying and doing things that excite the fans; it's another thing saying something that will alienate you from every single sponsor and brand. I don't see that as the point."

David Haye career highlights – in pictures

"With what Fury said, no big brand on the planet will want to go anywhere near him because it reflects badly on them. I understand hyping the fight up and getting controversial, but I didn't see the connection, the financial connection. All he did is harm his brand and harm Tyson Fury as a fan-favourite fighter.

"Personally, I don't take it too seriously, and it seems to work out OK when I do that. I haven't lost any endorsements over anything that I've said or done, but as I've got older I've mellowed out, and because I'm a former champion I don't need to tell people how great I am, they know. They've seen me fight, they've seen me win world titles at multiple weights, so they know I'm the real deal."

No big brand on the planet will want to go anywhere near Tyson Fury because it reflects badly on them

Indeed he is – and not just in the ring. He's lucid in front of the camera, too, which probably comes from a brief flirtation with modelling when he was still an amateur boxer. "I was spotted by Bruce Webber when he was shooting for Abercrombie & Fitch. I was about 18," says Haye. "He came into the gym to shoot a bunch of his models and he saw me there. I was obviously topless, doing my thing on the bag, and he asked if I'd ever thought about doing modelling. I said 'Not really – I'm a boxer. I'm going to be the heavyweight champion of the world.'

Photography by Dan Kennedy

"He goes, 'Well if you want to do some modelling, I'd love you to get involved in this campaign.' I think he gave me £500 a day, and at that time that was great money for a young amateur boxer – that could buy a couple of new sets of gloves, travel to and from the gym for three or four months. I met some good people, and he got some great pictures out of it. But obviously when I was going to castings with a black eye, the agency I was with was like 'Could you try to keep this boxing stuff on the back burner?' I was like 'No, not really.'

"There's no undisputed champion of modelling – you don't really get the credit and the credibility, the pat on the back in the pub because you look pretty in a photoshoot. It worked out great for me, but modelling wasn't something that I really enjoyed. The way I saw it, it was a way to earn easy money without getting punched in the head."

Despite that, he's definitely retained his confidence in front of the camera, with a tousled grown-out afro replacing the corn rows he made his trademark, and an electric blue suit tailor-made by Timothy Everest.

"I like to try and look at my best, as I've grown older I definitely want to look a little sharper. When I was younger I generally couldn't care less about how I looked and how I dressed; I just wore whatever was at the top of the pile and clean. I thought whatever I do in the ring is what counts. But I realised that in years to come people will look back at pictures of me. Look at Frank Sinatra or Sammy Davis, or even Muhammad Ali – they always looked sharp; there were no pictures of them sitting around in ripped jeans and a T-shirt. They always looked immaculate.

Haye Day Hospitality Package

Haye Day Hospitality Package

If you want to enjoy David Haye’s Haye Day event on 21 May in real style, opt for the hospitality package, which includes:

  • Tour of the Muhammad Ali exhibition
  • Drinks reception and canapés
  • Three-course dinner with wine
  • Ringside seats for the action
  • Access to the official Haye Day afterparty at Brooklyn Bowl London
  • Haye Day goody bag, which includes a signed David Haye fight programme

For more info or to book, call 020 7587 0735 or email hospitality@hayemaker.com

Photograph by Eddie Keogh

"I like to have a tailored suit because of my body shape," he continues. "It's impossible to go into a store, pick something off the peg and it look decent on me. It has to be tailored, because I fluctuate in weight so much – my waist goes from a 36 to a 38 in a couple of weeks and vice versa, my chest goes from a 44 to a 46, and I find myself with three different wardrobes depending on my phase of training. So tailored suits are definitely a must for me."

The suit matches the man – and he's even bringing that same sense of showmanship into his fights these days – he and his team recognise the fact that, especially with a heavy hitter like Haye, the main event has the potential to be over in a matter of seconds, and they've built a comprehensive programme that spans music, entertainment and dinner – and lasts until the early hours to ensure an experience that transcends just the fight itself, which they've branded 'Haye Day'.

"Guests will arrive at about 6pm," he says, "they have dinner, and there's entertainment there as well. They go to the banqueting suite and then get ushered to their seats. They go and watch a couple of fights, they have music acts playing just before the main event – my fight – then after that they go to an after party and then go home very happy.

"That means from 6/7pm all the way through to 4am, they've got a full night of entertainment. I want it to be more than just a boxing match, because a boxing match could be the best 12-round fight they've ever seen, or it could be a one-round knockout. You never know, so with that being the case you want to make sure that even if the boxing is a one-round knockout, your guests have a night of entertainment, loads of pictures, sitting among celebrities, and lots of people who know the difference between a regular boxing match and a mega event."

All of this points to a man who has learned all there is to know about the way this sport functions. The modern-day Haye is calculating; he's considered; he knows how to work the mechanics of boxing not just to his own end, but to the fans', too. It might have seemed unthinkable when he exploded onto the scene ready to take on all comers, but, as a few hours in conversation with him confirms, this is a man who's permanently two steps ahead. In a sport punctuated by flurries of punches and outpourings of heat-of-the-moment emotion, and in an environment where so many have lost their heads, David Haye seems to have thought of pretty much everything.