Eddie Redmayne, Benedict Cumberbatch, Tom Hiddleston, Laurence Fox … the ever-growing list of public school-educated actors dominating British film and television is often offered as proof that posh actors are squeezing out working-class talent. Acting, some fear, is increasingly the preserve of those with cut-glass accents whose parents can afford to bankroll them when starting out.

Further evidence of the struggles that those from more modest backgrounds face comes from Dame Judi Dench, who has told the Observer that she receives countless begging letters from aspiring young actors asking her to help fund their training.

The Oscar-winning actress said: "Anyone who's in the theatre gets letters countless times a week asking for help to get through drama school. You can do so much, but you can't do an endless thing. It is very expensive."

Dench, considered one of the greatest thespians of her generation, added that since the demise of repertory theatre – "where you went to learn and make your mistakes and watch people who knew how to do it" – financial barriers to training have made the profession more elitist.

The actress, who won an Academy award for her performance as Elizabeth I in Shakespeare in Love, believes it is vital for young actors to watch professionals on stage. "I always say to young students, 'Go and see as much as you possibly can', which is what we used to do. But then we paid a pittance for sitting in the gods," she said.

Ideally, she said, she would reinstate reps all over the country, but knows this is impractical, though she does not believe that government has to choose between hospitals and theatre: "In a civilised country, there's money for both."

She accepts that talented aspiring actors can make it without going to drama school. "But it's a hard and rocky road," she added.

Her comments follow those of Ben Stephenson, the BBC's controller of drama commissioning, who, at the Edinburgh international television festival last month, said acting had become too much of a middle-class profession. He argued that entry was too expensive for those from disadvantaged backgrounds. His criticisms were echoed by Vin Harrop, a "secondary modern boy" who worked his way up to head the Council of Regional Theatre before entering BBC management. In a letter to the Daily Telegraph last month, he said: "When we had repertory theatres … people from all sectors of society took to the boards. It is a sad state of affairs when [most] actors come from the so-called 'posh' schools."

Those schools include Eton, whose old boys include Redmayne, Damien Lewis and Dominic West – best-known for television dramas Birdsong, Homeland and The Wire respectively – and Harrow, where Cumberbatch, star of the BBC's Sherlock series, and Laurence Fox, best known for his role in Lewis, were educated. Max Irons, who went to Bryanston School in Dorset, plays the lead in The Riot Club, a film version released this week of Posh, Laura Wade's satire about Oxford University's Bullingdon Club that was staged at the Royal Court in 2010.

Similar concerns were recently voiced by Sir Peter Bazalgette, the Arts Council chairman, who believes actors from public schools are "out of proportion", and Brian Cox, one of Britain's foremost actors, who lamented that acting was "cutting itself off" from working-class Britain.

Edward Kemp, artistic director of the Royal Academy of Dramatic Art (Rada), told the Observer that 36% of last year's students came from families with an annual income of less than £25,000. He said Rada offered bursaries and observed that the money was going to the "squeezed" middle classes, adding: "You can be earning £50,000 and have two kids in higher education and there's very little support. That's the danger area."

Kemp also spoke of a "serious worry" since the loss of repertory theatre. For those outside London, he said, "the chances of being exposed to really good theatre is getting squeezed. Facilities for drama in most private schools way outstrip any state school."

Sources say that Dench has supported students "discreetly" at the Royal Central School of Speech and Drama, where she trained, as did her brother and daughter. Gavin Henderson, the school's principal, said: "She's been enormously supportive. She was for a period president of the school. She was deemed to be generous. She came back recently and did a session with the students. She's been back several times. When we need support on certain issues, she's always very quick to come forward."

He added: "We haven't seen at Central any noticeable shift to the 'better off'. The biggest fear is what's going on in schools now, and the way in which the arts and humanities have been downgraded in schools. So it's the motivating of students from disadvantaged backgrounds towards the notion that a career in the theatre is worth pursuing. That's where the biggest problem lies."

Of course some will always find a way. Tom Courtenay, who won Oscar nominations for Doctor Zhivago and The Dresser, told the Observer that he financed his Rada training partly by working as a labourer to supplement his grant. Asked whether today's aspiring actors need private wealth, he said: "Whether they do now, I can't say. Certainly they didn't in the 1960s. John Thaw [the late Morse star] and I didn't come from money and we did all right."

Cassie Bradley: as well as part-time work, she needed a DaDA award to attend drama school. Photograph: Faye Thomas

Hard act

Cassie Bradley has a degree in English literature from Durham University and graduated from the Oxford School of Drama last summer. She went on to appear in Sam Mendes's production of King Lear at the National Theatre. She could not have trained as an actress without the support of the Dance and Drama Awards (DaDA) scholarships, awarded to trainee actors and dancers.

"It was very difficult. I'm from a single-parent family in inner-city Nottingham. I couldn't have afforded to go to drama school without the DaDA support. Mum was talking about remortgaging the house. I also had three jobs while I was at drama school [for three years]. I worked all summers, holidays, as well as having a weekend job while I was there. I worked in a clothes shop, a restaurant…

"A lot of us don't go into this profession because we think we're going to earn a lot of money or become famous. We do it because we love it and we're passionate about it.We're as passionate as people who want to teach or become nurses. If you don't invest in people's training, it's going to have such a huge effect on not only our theatre industry, but also our culture."