It's funny how things turn out. It's a Wednesday afternoon and I'm sitting in Soho House, Dean Street, waiting to catch up with an old schoolmate. Only the thing is, the man in question is an actor who's fast approaching A-list status, and the 'catch-up' is an interview for the cover of the magazine I write for.

I spot him through the window on his way in, my mind conjuring up images of a teenager in a school blazer eating a crisp butty, probably on the other end of the occasional jibe about his model good looks. But 2016's Douglas Booth is a very different proposition: he's an actor who has won acclaim for his breakout portrayal of Boy George in the BBC's Worried About the Boy; been voted GQ and Hugo Boss's Most Stylish Man; co-starred alongside Mila Kunis and Russell Crowe; and been directed by Darren Aronofsky and the Wachowskis, among others. And I thought I'd had a productive few years since graduating.

Booth is calm and measured when he talks – a likely combination of a natural humility and a good few years of press junkets. "I try not to think about it too much," he says, when I ask the extent to which he's aware of his own rapidly growing profile. "For me, the level it is right now is manageable. A very successful actor I once worked with told me 'Enjoy this period. At this point you can get reservations at restaurants – you can get lots of perks, but you don't get the crazy negatives.'"

"I remember being at the Met Ball a couple of years ago," he says, when I ask him if it ever gets a little surreal. "You've got Paul McCartney and Fergie from the Black Eyed Peas jamming in the hallway. Rihanna walks past like, 'Excuse me, sorry.' Then you're in the toilets – everyone smokes in the toilets at the Met Ball because you can't go outside – with Eddie Redmayne and Domhnall Gleeson, and then Johnny Depp comes out one of the cubicals and is like, 'Get me the fuck out of here, man. Can I have a cigarette?'"

"Anonymity is an amazing thing, and I've already grown to appreciate that. But I am not going to sit here and complain about fame and sound ungrateful – as long as you keep all your friends and family around you and try to keep your feet on the ground, that's all you can do."

I do work that I think I can get my teeth into – or the cast is great. It has to give me something

Given the speed and scale of this young British actor's rise to prominence, keeping grounded must be no mean feat. Back in 2009, he was auditioning for everything going, with only a few callbacks. Roles in From Time to Time and The Pillars of the Earth followed, as well as a brief flirtation with modelling in a 'young actors' campaign for Burberry – alongside Emma Watson, with whom a close friendship was formed – before the game-changer: the lead in the BBC's biopic of the Culture Club, a taste of Booth's chameleonic potential in a role so far outside a young actor's comfort zone I assumed it had to have been a calculated move. It wasn't, as it turns out: "I was just looking for a job," Booth admits. "I was 16, going on 17. It came along and I was like, 'Boy George, really?' I ran to the computer. I remember my mum and I typed it in and looked him up."

It turned out to be a huge success, winning the young Booth enormous acclaim in a role that likely entailed near method-actor preparation. Even the singer himself was effusive in his praise, telling the BBC Booth had "the stink of me". In fact, Booth describes just how much the role played with his sense of identity: "It was one of the most transformative things for me ever – I literally felt like I was him in this weird place. I remember him walking into the room when he came to visit the set and it was really emotional because I was thinking 'How can he be standing there when I'm here?'"

His detractors may point out that, in the four years since, Booth hasn't followed Worried About the Boy up with a project that shows his range to the same extent. But he is assertive about his career choices – ones that include a range from low-budget independent releases to supporting roles in big studio epics Noah and Jupiter Ascending. I ask him whether it's a case of the mantra 'one for the studio, one for you', where actors in effect pay for their involvement in lower-budget passion projects with larger, box-office sure-things. George Clooney is arguably its most devout follower. Booth is bemused, possibly having not considered this before, and says of both films that the chance of working with genre- and era-defining directors was just too good to ever consider turning down: "For me, I wanted to work with Darren Aronofsky, who is one of my favourite filmmakers. The biggest movies I've done have been completely driven by wanting to work with the directors.

"I remember when Jupiter Ascending came round, I had the opportunity to do one of the big, better-known YA [young-adult] franchises. I didn't think the script was very good – it wasn't as good as The Hunger Games. So I asked Darren Aronofsky, 'What do I do? Do I do this or do I work with the Wachowskis?' He was like, 'Work with the Wachowskis.'"

Douglas Booth in his latest film, Pride and Prejudice and Zombies

Douglas Booth in his latest film, Pride and Prejudice and Zombies, in which Jane Austin's romantically tangled characters are faced with brand-new obstacles, namely the un-dead. Take that, Mr Wickham. 

With good reason. For a young actor, the chance to work with the filmmakers who rocked sci-fi with The Matrix in 1999 is one that should certainly be taken. "Even though Jupiter Ascending wasn't received particularly well," he says, "I think that as time goes on it will definitely get more of a cult following. I'm so glad I made that decision to work with them, just to see how they work. After all, they changed the way movies are made.

"I don't really do 'one for me and one for them'. I just try and do what interests me and sometimes things work and sometimes things don't. I do work that I think I can get my teeth into – or the cast is great. It has to give me something. I'm 23 years old, so I'm really not rushing my career. I am lucky enough to be in a place where I don't have to take work for the sake of it. I just want to have done interesting stuff by the time I get to that late-20s age where you come into your own as a leading man. I'm trying to build up a CV, work with interesting people, and get to a place by my late-20s where I have learnt and I am ready."

I can't help but feel Booth reminds me of someone. Someone who is known for being selective in his projects, for his humanitarian efforts, who also played the lead in a film adaptation of Romeo and Juliet. I ask whether there's anyone whose career he'd emulate, in his own way, if he could, and his answer confirms it: "Not that I expect my career to be anything like his," he says, "but if you look at Leonardo DiCaprio, for me that's someone who is just completely classy. I would really love to have the opportunity to work with a few very good filmmakers consistently, to build up those relationships and to go on adventures like that. I think he balances his critical and commercial success very well."

I don't know whether Booth and DiCaprio have met – I forgot to ask, sorry – but I'm sure Leo would be impressed at Booth's role in publicising the need for action on some huge issues, including speaking on behalf of longtime friend Watson's HeForShe gender equality movement, and being an ambassador for the UNHCR, the UN's refugee agency. The position came about when Booth was preparing for a possible role in a biopic about photojournalist Dan Eldon, who died in tragic circumstances on a humanitarian mission in Somalia. He describes an encounter around that time with a Syrian refugee in Lesbos, Greece, with the UNHCR, that made standing idly by a non-starter: "It sounds dramatic to say it changed my life, but it really did change my opinion and my outlook on the world and what was important. To sit there opposite someone my own age who had everything going for them – more intelligent than me, a better degree, better jokes, more charismatic – this man had everything going for him; the only difference is that he was born in a country that's now ravaged by civil war, and I had the great fortune to be born here. He was in such a difficult, desperate position, but he was dealing with it with such grace. It changed my life and changed what was important to me."

The industry is quite small and incestuous here – I go to work with a bunch of my friends

Today, though, Booth could be forgiven for thinking of himself first. He's promoting his latest role – in Burr Steers' adaptation of bestselling mashup novel Pride and Prejudice and Zombies. The film is a delight – a splicing of the fusty British period drama with the absurd but brilliant addition of a zombie outbreak, which makes for a rollicking comedy-thriller that never takes itself too seriously. "I was sent a script and I thought the idea sounded barmy," says Booth. "'Pride and Prejudice and what?' Then you suddenly realise that David O. Russell had written the first draft of the script. Then I looked at the book, which was a New York Times bestseller – it seemed to just be really popular. They attached an amazing cast; I met Burr in LA, we got on really well and I really enjoyed his vision for it, and that was it. Then I went to work with a bunch of my friends, which was wonderful."

The friends in question include some of Britain's most exciting up-and-comers, whom Booth has worked with on a few projects, including TV adaptations of Great Expectations and the recent And Then There Were None. "The acting industry is quite small and incestuous here. On Pride and Prejudice and Zombies, I worked with Matt Smith, who is also one of my very good friends. Lily James I'd known because she went to drama school with one my best friends Freddie Fox [whom Booth starred alongside in The Riot Club and Worried About the Boy]. I remember seeing her in her drama school productions and she was just great. I remember looking at her thinking, 'She is going to go somewhere.' And she has."

It all points to a golden age for Britain's band of young actors, of which Booth is becoming a standout. How closely his career will emulate DiCaprio's is academic – the reality is that he seems set to enjoy a career similarly driven by personal and artistic ambition over money, which will be punctuated by moments he uses his industry prominence to do some extraordinary things – on- and off-screen. As for me, I make him promise me another interview in a few years, when he steps into whichever lead role transforms him from a supporting actor to a leading man. Whatever happens, one thing's clear – he'll do it on his own terms. ■

Pride and Prejudice and Zombies is out 11 February. To learn more about the global refugee crisis, see our sister title Escapism's special report at escapismmagazine.com/the-refugee-crisis