The UK's black stars are succeeding at the American box office – but are they working there because some parts offered in the UK are off limits, while others play to stereotypes?

When Resident Evil: The Retribution, starring Milla Jovovich, is released in cinemas in the autumn the arrival on screen of the man they call One, the mysterious leader of a commando unit, may surprise British audiences. And not just because he was chopped up into pieces by a laser in the first of this franchise of American action films. No, the reappearance of One is unexpected because he is played by British actor Colin Salmon, also known to television viewers from the ITV1 show Law and Order: UK, among many other popular homegrown television drama series.

Salmon, 49, is one of a growing group of distinguished black British stars making big budget US film and television projects to supplement a British acting career. But whether black talent is drawn to Hollywood by the money, or by the more substantial roles on offer, is not clear.

Last week David Harewood, 46, the acclaimed Birmingham-born actor who played Martin Luther King in The Mountaintop on stage in London in 2009, criticised the British TV industry for failing to take risks with black casting. He was speaking in London at the launch of Homeland, the Golden Globe-winning US thriller series shortly to be aired on Channel 4.

"Unfortunately there really aren't that many roles for authoritative, strong, black characters in this country. We just don't write those characters, that's a fact," he said. "I don't want to trash this place, but I do think there is a certain lack of ambition in terms of telling a global story."

Like Salmon, who has made regular appearances in the US TV show Single Ladies, Harewood has gained kudos from crossing the Atlantic for a role in a TV hit. Fellow black actors Idris Elba and Adrian Lester have both executed a similar manoeuvre. Elba has just won a Golden Globe for the British show Luther, but first made his name in The Wire, while Lester, who returns to the National Theatre next year to play Othello, has appeared in Hollywood-made films and TV shows such as Girlfriends, the sitcom produced by Kelsey Grammer.

"It's not possible to sustain a film career just by working in Britain. Black or white, whoever you are," Lester said last year.

London born and bred Chiwetel Ejiofor, who received a Laurence Olivier Award for his Othello at the Donmar Warehouse in 2007, has punctuated his stage roles with Hollywood work too, notably in the films Salt and 2012. Another acclaimed star of the British stage, David Oyelowo, the first black actor to play an English king in the Royal Shakespeare Company's 2001 Histories series, starred in last year's release The Help and now has a part in Steven Spielberg's Abraham Lincoln biopic to occupy him. It is a career path already taken by Marianne Jean-Baptiste, who went from Mike Leigh's Secrets and Lies to the hit US television show, Without A Trace.

Yet the strong evidence that worthy parts come only to those black actors who travel is disputed by the iconoclastic US director Spike Lee. Speaking at the Sundance film festival last week, Lee said he had made his latest feature, Red Hook Summer, with low-cost kit partly to avoid Hollywood. "They know nothing about black people," he said, questioning how Hollywood producers could have any idea about the area of Brooklyn where his film is set. "Fuck no! We had to do it ourselves!" he concluded.

Lee's words echo those of Viola Davis, the Oscar-nominated US actress who stars alongside Oyelowo in The Help. Last autumn she told the Observer: "We're made up of so many different pieces of a puzzle as human beings and I find that when you're a black character, you only have maybe seven puzzle pieces to work with all the time… Really all you have is funny, strong, sassy, dignified, wise, and that's pretty much it."

Last month Pam Grier, the veteran US star of 1970s blaxploitation movies and a Golden Globe-winner in the lead role in Quentin Tarantino's Jackie Brown, made the same point. Speaking in Toronto last week, she said: "I know a lot of African American women that didn't want to see The Help because they had lived it as little girls and it was a circumstance that shouldn't have been and it was so problematic for them. It brought back horrible memories and they couldn't see it, nor will they read the book," she said.

Star Wars director George Lucas has also recently complained about how hard it was to raise the money to make Red Tails, his film about black US airforce pilots, because there were no white stars. The film, which also stars Oyelowo, was eventually completed, however, and made $19m at the box office on its opening weekend in the US last month.

Since Hattie McDaniel won the first Oscar for an African American with her part in Gone With The Wind, black actors in Hollywood have had to struggle with the accusation they are taking stereotypical roles, drawn up by white men. But British actors seem to have no such fears. The issue is all too clear, according to Harewood: "I can remember talking to Idris years ago about these frustrations and he told me 'I'm going to America' and I kind of thought, 'What are you doing that for?'

"Look at him now. He's a huge star; he made the right decision, even though it took him a long time to crack the US. I knew what I needed to do. I simply wouldn't have been given a role of that strength and authority in the UK."

British actor Giles Terera, 35, who has played Sammy Davis Jr in the West End as well as appearing at the National Theatre, has heard this advice many times. "A friend of mine who has just come back from LA said to me what black actors always say: 'Go out there and get parts rather than just playing another drug dealer or mugger over here'." But Terera is happy with the mix of work he finds in Britain. "I can do the work that suits me, but it is true there is an issue here that goes very deep."

Terera has noticed that while actors of mixed race are cast in black roles, they are not cast in white roles. "It is all to do with what audiences will accept, as much as to do with directors and casting directors," he said. "Sometimes I am frustrated at the parts white friends get, but it is more difficult to be black anyway, not just in the theatre. When I want to hail a taxi in London, I know it's going to take three or four before one will stop for me."

Terera played Horatio in Hamlet at the National last year and remembers a friendly, older white audience member explaining to him that Horatio would "never have been black in real life". The actor, who is 35, felt like pointing out that the cast were also all speaking English, not Danish. "It is all about suspension of disbelief again," he said this weekend. "A lot of people feel like David Harewood, because you can feel excluded from a whole area of casting, say from that Sunday night costume drama area. It is off limits."

Cush Jumbo, 26, star of the National's new production of She Stoops To Conquer, is more optimistic. "The majority of roles I have played so far have been classical and that is not what I expected, growing up in Lewisham and having a bit of a south London accent. And I hope it was not because the director wanted to make a statement."

Jumbo, who attended the Brit School before going on to Central School of Speech and Drama and who appears in ITV's crime series Vera, believes there is good television work for black talent in Britain too. "I understand what David Harewood is saying, though, because there is so much good quality television made in America. Here it's about having an agent who will push you towards roles that are non-colour specific.

"When I go back to the Brit School to talk to kids, especially to black kids, I tell them to make themselves the most versatile actor they can. That way you can give them 'the kid from the council estate', if they want, but you can also give them Shakespeare's Rosalind."