I’m on the way to meet Antonia Thomas in a Peckham cafe when who should I spot but Antonia Thomas, sitting at the window of a Peckham cafe. Par for the course, you might imagine, except the interview isn’t for another half hour and she’s at the wrong cafe.

Or is she?

Once I’ve checked my email and confirmed I’m not experiencing some form of early onset dementia, I’m left with a bit of conundrum. Do I continue onto Petitou, the agreed venue, and wait for her arrival, or pop into Rosie’s and say hello?

My vacillation is cut short when Thomas emerges from Rosie’s and walks off in the opposite direction to me - and, more alarmingly, to Petitou. Since chasing your interviewee down the street is frowned upon in journalistic circles, I resolve to continue with the original plan and assume she’ll show up eventually. Stiff upper lip and all that.

“You should have come in and said hi!” Thomas tells me half an hour later. (Turns out her house is undergoing maintenance work - boiler, I think - and she was killing time round the corner from our rendezvous.) I probably should have done: it’s a hackneyed old line but Thomas really is one of the nicest and most grounded interviewees you could share a coffee with, and it seems unlikely an impromptu hello would have disturbed her inner feng shui. (Or such was my impression: maybe there’s a lifesize Antonia Thomas statue in her hallway; maybe the house ‘maintenance’ was actually its installation.)

I’m just sat there grinning, thinking, ‘Oh God, I've fucked it up!

I mention the above mix-up partly as an amusing anecdote to open the article, and partly to juxtapose it with a not-entirely-dissimilar anecdote of Thomas’s - another story of missed cues, uncertain etiquette, and the importance of ploughing on regardless.

At the start of the year Thomas appeared on Jimmy Kimmel Live, her first time on an American talk show. She’d prepared her opening story - it involved messing up an American accent mid-audition - and rehearsed it with one of the production team. (Guests don’t actually meet Jimmy before broadcast.) There’d be a couple of questions to tee her up, and then bam - take it away, Antonia.

Kimmel asked the first question - “You have to get the accent down just for the audition, right?” - and she kept her powder dry, waiting for the second one - which never came! “He obviously went, 'she's not going for it', and moved onto the next story. And I’m just sat there grinning, thinking, ‘Oh God, I've fucked it up!’ I don't think it comes across that way,” she adds. It didn’t: I checked out the YouTube clip, and basically never play poker with Antonia Thomas. The smile never left her eyes.

It’s funny to hear Thomas namedrop Jimmy Kimmel. After an hour in her company, discussing such thespian hot topics as the cost of living, South London nightlife, and the art of never growing up, it’s easy to forget that these days she’s a Big Deal thanks to her role in The Good Doctor, a show proving a hit on both sides of the Atlantic.

The Good Doctor is the latest incarnation of the big, glossy medical drama that American TV does so well. (House creator David Shore is an executive producer.) The show focuses on a young, brilliant surgeon with autism and savant syndrome, played by the perpetually boyish Freddie Highmore, and his colleagues at San Jose St. Bonaventure Hospital - including Thomas’s Dr Clare Browne.

Deftly tackling a number of weight topics - social and ethical, as much as the classic medical ‘THIS BOY HAS THREE HOURS TO LIVE’ - the first two season have brought strong ratings and critical acclaim. However Thomas nearly missed out on the biggest roles of her career to date.

She’d flown to LA for pilot season: the period of the year, roughly from January to April, in which studios film pilots of TV shows and then decide if these shows will be picked up. As Thomas describes it, “Basically actors descend upon LA – even more actors descend upon LA – to try and get a job. It's generally a bit intense because there's so much casting and so little time to prepare anything.”

Went in to audition feeling a little bit foggy headed, thinking I didn't have a chance

If the audition goes well, you’ll be asked to sign a test deal: which basically stipulates that you’ll take the role if offered it - regardless of what other, more attractive roles you might be offered after putting pen to paper. Game of Thrones? Can’t do it, pal: you’ve already committed to CSI Toronto. Exacerbating an already fraught situation is the fact you’ve no real idea whether the show you’re about to go exclusive with will turn out to be any good; meaning you could turn down the next Friends for a brief stint on the next Monty. (Both mid-nineties sitcoms starring David Schwimmer. One was cancelled after six episodes; the other wasn’t.)

After several weeks of audition, audition, audition, make a potentially career-defining decision, audition, audition, you can hardly blame Thomas and her friend Ruth for letting off steam over a few cocktails one Friday night. A couple of drinks in, the agency rang. “So, there’s this other pilot, and they’re casting tomorrow morning…”

Thomas rushed home to cram the script. “Went in the next morning feeling a little bit foggy headed, thinking I didn't have a chance.” Funnily enough, she attributes this mindset as a possible factor in her landing the role. “If you can bottle that quality – not nonchalance, because nonchalance is the wrong word, but a lack of pressure. I didn't put any pressure on myself because I didn't think I was going to get it.”

The Good Doctor is the latest chapter of a story that began nine years ago with cult superhero comedy Misfits. Thomas walked out of drama school and into the role of Alesha Daniel, a teenage delinquent who provokes insatiable desire in anyone she touches. (That’s literally her superpower - one of the milder superpowers on display. You should watch Misfits.)

She was initially sceptical about pursuing the role - swapping three years of Shakespeare for sexual escapades in an orange jumpsuit - but every audition the sheer quality of the script proved impossible to resist. The public agreed: Misfits was a breakout hit and made stars of its young cast, including the most evil man in Westeros, and former Square Mile cover, Iwan Rheon.

“It was so fun, it was so fun,” she says of her time on Misfits. “It was kind of a joyous experience. We were all so hilariously different as people, and most of the time gelled, and sometimes fought – but it was just brilliant. It was just brilliant. I've realised since, almost ten years later, you don't get jobs like that that often - where everything is great. We were like siblings.”

Three years after leaving Misfits she landed another dream gig in another quintessentially British comedy, albeit one that couldn’t be further from foul-mouthed teenage superheroes inadvertently saving the world. (There’s a significantly lower body count, for starters.)

Lovesick is a very sweet sitcom that pivots around a failed chlamydia test (stay with me). Idealistic, romantic Dylan tracks down an extensive list of ex-lovers (for a man so committed to finding ‘The One’, Dylan sure did shag around) to reminisce over What Might Have Been and suggest a visit to the clinic mightn’t be the worst idea. (The first season was called Scrotal Recall. When Netflix picked up the show from Channel 4 the title was quietly amended to something that didn’t make its cast wince when brought up in polite conversation.)

As Dylan’s close friend / ongoing love interest Evie, Thomas is the standout member of an excellent ensemble - every sidelong glance a silent monologue of conflicting emotions. Lovesick was made by the same production company as Misfits, and her time on the show sounds equally idyllic. “We all just had a laugh, frolicking around in Glasgow,” she recalls. “Every weekend we'd go disco dancing – I can't think of the last time in London that I went dancing.”

When I was in my teens I used to think that by 30 I'd have my shit together

Dylan is played by actor and musician Johnny Flynn. (He composed the theme to Detectorists, another brilliant British sitcom.) His casting gave Thomas a minor dilemma.

“I was a superfan of his music, had all of his albums. When Johnny got the part I thought, ‘fuck, I'm going to have to normalise this’. The first time we met I was like,” (and here she starts talking at double-speed) "’I just have to say I'm a really big fan. Just wanted to get it out of the way. Let's not talk about it, we don't have to talk about it, it's not weird, I'm just a really big fan. OK. Let's move on.'”

Awkward dates, financial worries, career uncertainty - Lovesick very much captures the muddle that can be the late twenties, when you’re almost a Proper Grown Up but you can’t quite take the last step, or even work out what the last step might entail. Like most of us, Thomas relates. “When I was in my teens I used to think that by the time I'd be 30 or almost 30 I'd have my shit together, I'd know what I was going to be doing, I'd have a house, whatever. And actually, it's just not the reality.”

Well, she had to wait a couple of years but the house has finally been procured. There’s a pleasing thread of growth running through Thomas’s work: the spiky adolescent of Misfits becomes the unmoored twenty-something of Lovesick becomes the accomplished medical consultant of The Good Doctor. However, like many black British actors, she found limited opportunities in her home country - hence the need to audition in LA.

This is an ongoing trend: in recent years a number of black British actors have migrated to America. Ricky Whittle, Idris Elba, and David Harewood all landed plum roles in US shows after finding precious little work this side of the pond; while Daniel Kaluuya, John Boyega, and Chiwetel Ejiofor are better known for Hollywood blockbusters than appearances on British screens.

She cites the British obsession with period dramas (which she loves) as a factor in this lack of diversity - where casting such as James Hewson’s 2011 Heathcliff tends to be the exception to the rule. “One of the reasons I'm doing The Good Doctor is that I felt there was more opportunity and work in America. But it is changing. That is changing. It's just a slow process.”

There are hundreds of stories, it's just about the stories that people want to tell

Thomas intends to speed up this process by becoming more involved in the creative process, telling her own stories. She and Chuku Mundo, her co-star in The Good Doctor, recently collaborated on the short film Freedom's Name Is Mighty Sweet. It tells the story of Charles and Lucille Baker, an African-American couple who decided to do the Gold Rush, travelling from the Deep South to the Yukon wilderness despite Lucille's pregnancy. It's an epic tale and, with all due respect to Jane Austen, sounds considerably more appealing than yet another retelling of Pride and Prejudice ('this time set in space!').

What's important, as Thomas notes, is "the people telling the stories need to be rainbow coloured. And the people at the top, commissioning things, need to be much more diverse. So many more women too: diverse in every way."

She’s spoken of her desire to adapt the story of another “superwoman”: her mother Veronica, who moved from Jamaica to Yorkshire aged 11, and suffered precisely as tough a time of it as you would imagine - 1960s Yorkshire not exactly being a hotbed of cultural integration. Undaunted, Veronica became an NHS nurse, fought her way up the system, and retired this year as head of psychology at St Thomas's Hospital. Great films have been made from weaker material.

"There are hundreds of stories," says Thomas, "it's just about the stories that people want to tell."

Hers is far from finished. And it’s turning out very nicely.

Watch The Good Doctor at Tuesday 9pm on Sky Witness or catch up on NOW TV.