The invasion of British and Irish leading men in Hollywood has now gone beyond a joke for many in the American entertainment industry. First noticed some time in 2011, the trend was initially dismissed as a novelty: an interesting phase that would pass, rather than as a threat. But this summer actors and directors are calling for action to mobilise American drama teachers and schools to counter it.

In Britain, of course, the same trend is greeted gleefully as another chance to cry out, “the Brits are coming!” One by one, each wave of the invasion has been characterised and cheered off at the dock.

First, a group of talented black stars, including David Harewood, of Homeland, and Idris Elba, of The Wire, felt they had a better chance of good roles and good pay in Los Angeles. Then, a slew of superhero signings was spotted; the British-raised Andrew Garfield was cast as Spider-Man, Welshman Christian Bale as Batman, and the Stowe-educated Henry Cavill as Superman.

Next, came a third onslaught of what might have sounded like the posher, officer class; the old Etonians: Hugh Laurie, in House, Dominic West, in The Wire, Damian Lewis, in Homeland, and Tom Hiddleston as Loki in the Marvel comic book films – except, of course, these well-heeled English actors’ tough American accents and stateside machismo were faultless when required.

Then, the Welsh infantry arrived, with prominent television roles going to Michael Sheen in Masters of Sex and Matthew Rhys in The Americans. Four years on, it turns out that this was not a shortlived fad. Britain is still sending regular reinforcements across the Atlantic, from the new Spider-Man signing (Tom Holland from Surrey), to the actors who have recently snatched real-life national archetypes like Abraham Lincoln (Daniel Day-Lewis), Ernest Hemingway (Clive Owen) and Martin Luther King (David Oyelowo) from the grasp of American stars.

And that is to say nothing of the upcoming movies in which Irishman Michael Fassbender will play tech-guru Steve Jobs, Hiddleston will play country singer Hank Williams and Bedfordshire’s Ben Whishaw will play Herman Melville, author of America’s most revered novel, Moby-Dick.

A serious backlash has started in America, with film-making heavyweights such as the actor and producer Michael Douglas and the director Spike Lee calling for an urgent rethink in the industry. Both have asked why their country is failing to producing male stars with heft enough to tackle more of the major roles.

Is acting no longer considered a manly profession, some have wondered. Douglas has spoken of a “little crisis going on among our young actors at this point”.

Lee put it down to the skills that British actors learn. Their training, he said, “is very proper, whereas some of these other brothers and sisters, you know, they come in here, and they don’t got that training”.

The resistance movement has been growing since January when Richard Hicks, president of the Casting Society of America, pointed out that a search for new faces had become an epidemic. “I went to see a movie,” he told Entertainment Weekly “and four casting directors were sitting around talking about, ‘What’s up with all the Brits and Australian actors snagging all the leads?’”

Vince Vaughn in True Detective. Photograph: Lacey Terrell/HBO

Hicks and his colleagues put the problem down to a failure to train American actors in character work. It is by building up a portfolio of cameo roles that a talent can develop, he argued. In answer to the dearth of substantial male talent, his fellow casting directors cast their net wider, giving serious roles to actors who had picked up technique in comic roles. So Steve Carrell was cast in Foxcatcher, Adam Sandler in Punch Drunk Love and Funny People, Ben Stiller in While We’re Young and now Vince Vaughn stars in the bleak second season of the hit television series True Detective.

Not everybody in America is upset, of course. In the Chicago Tribune this month a pundit praised the skill of British actors at faking American accents. Sometimes, she said, it was almost distracting how good Elba’s Baltimore street talk was in the hugely successful The Wire.

Cecilie O’Reilly, a coordinator of voice training for Columbia College Chicago’s acting programme, has worked with British actors and the trick is, she said, to teach them to master the hard “r” sound and to form vowels differently, moving pressure away from the roof of the mouth. British actors, O’Reilly added, are happy to switch vocal techniques and are prepared to study.

“They come from a tradition of vocal skill and training. The Brits are steeped in a tradition, of many, many years of having the appreciation of the variations on their speech. And there is a pride in it.”

It is this question of pride that feeds into an emerging theory about what the problem might be for the US entertainment industry. In the American magazine the Atlantic last week the film critic Terrence Rafferty argued that homegrown young men had lost the ability to take acting seriously. “Crisis or not, this is getting embarrassing,” he wrote.

Others have argued that the big budgets of American dramas have meant that casting directors can afford to look across the English-speaking world for fresh talent.

There had been an earlier suggestion that perhaps British actors came cheaper than their US counterparts, but this was shot down when it emerged that Laurie was paid $18m (£11.5m) for his stint in the medical drama House.

Whatever the reason, figures for last year from the Department of Homeland Security show a 500% increase in the number of visa petitions approved for actors and directors from the UK who want to work in the US entertainment industry.

Method man Marlon Brando in 1954’s On the Waterfront. Photograph: Moviestore/REX Shutterstock

The influx of Brits has caused some, including Douglas, to mourn an era when a career in film was something to be studied for at the Actors Studio or the Neighborhood Playhouse, places where teachers such as Stella Adler and Lee Strasberg preached serious theory, such as Constantine Stanislavski’s “method” approach, which produced a “golden era” of American film acting and stars such as Marlon Brando, James Dean and Montgomery Clift and, later, Robert De Niro, Al Pacino, Dustin Hoffman, Robert Duvall and Gene Hackman.

Today, many actors – like the proficient George Clooney –acquire their training in television. The British director Stephen Frears is concerned that this is not always a good thing for the industry.

Four years ago, he told a BBC radio audience: “There is a kind of crisis in American acting. It is very noticeable.” He added: “If I were being tedious I would say it’s the lack of a theatre. When you work with someone like Annette Bening or Glenn Close, they are highly trained. It’s like working with Judi Dench. They are the real thing. But a lot of American cinema doesn’t have that background.”

It seems that younger American female actresses have also held their ground better. There is plenty of fearless, versatile talent around. Take your pick from Michelle Williams, Keri Russell, Jessica Chastain, Amy Acker, Kirsten Stewart, Jennifer Lawrence, Emma Stone, Reese Witherspoon, Elisabeth Moss, Dakota Fanning, Shailene Woodley, Rosario Dawson, Scarlett Johansson, Anne Hathaway, to Zoe Saldana.

And while there are some equally impressive younger male actors, such as Leonardo DiCaprio, Joaquin Phoenix, Channing Tatum and Matthew MacConaughey, they are thinner on the ground.

Hollywood has always been refreshed by British leading men. Some of the biggest names in its history, including Charlie Chaplin, Stan Laurel and Cary Grant, made the transatlantic journey in search of better work.

Even Eltham-born Bob Hope, the quintessential wise-cracking American star, used to recount that he had made his way over to the US by boat at five years of age because, “I felt I wasn’t getting anywhere in England.”

• This article was amended on 7 July 2015 to update the headline. An earlier version also said that Fred Astaire was one of those who made the transatlantic journey in search of better work. He was born in the US.

