David Tennant has been cast in Hamlet for the RSC
Theatre director Sir Jonathan Miller has accused West End producers of having "an obsession with celebrity".
The 73-year-old told The Times the obsession was causing theatre bosses to turn down acclaimed productions because they lacked a TV or film star.
He said he had trouble getting London producers interested in his latest productions because his cast had no famous names despite rave reviews.
Sir Jonathan has won numerous Olivier awards for his Old Vic productions.
One of the director's recent productions, Hamlet - which was staged in Bristol, received great reviews.
Critics hailed lead actor Jamie Ballard as an "exceptional talent", but the production failed to garner any West End interest.
"Producers might have been swayed if I'd been prepared to put in for more luminous names," Sir Jonathan said.
"But I wanted my original cast, who were absolutely first-class."
There are currently two West End versions of Hamlet in production - one starring David Tennant for the Royal Shakespeare Company - "that man from Doctor Who" as Sir Jonathan referred to him - and the other starring Jude Law.
Sir Jonathan Miller has won numerous Olivier awards
Speaking about Law, Sir Jonathan said: "I suspect he can't act better than the young unknown who played him for me, who was quite extraordinary."
Last year, London producers were interested in transferring the director's Sheffield production of The Cherry Orchard starring Joanna Lumley to the West End.
But when Lumley said she could not commit herself to a long theatre run, they backed out.
"I understand Sir Jonathan's frustrations," said Michael Boyd, artistic director for the Royal Shakespeare Company.
"It is something we have encountered with previous productions which we were keen to take into the West End."
But Boyd denied David Tennant was a "celebrity" Hamlet.
"David has not been cast because he is Doctor Who, but because he is an excellent actor who deserves to play the role of Hamlet," he said.
"He earned his spurs with the company for two seasons - in 1996-7 in A Midsummer Night's Dream, As You Like It and The Herbal Bed, and then returning in 2000 to play Romeo in my production of Romeo and Juliet and Antipholus of Syracuse in The Comedy of Errors.
"Of course, the fact that David went on to become hugely popular as Doctor Who and for his other popular TV roles, means that he brings with him audiences who would not necessarily have booked to see Hamlet which can only be a good thing," he added.
In a statement, Michael Grandage, artistic director of the Donmar Warehouse, said: "Both Jude Law and David Tennant have earned their spurs in classical theatre.
"I find it disappointing that in commenting on his own production of Hamlet, Jonathan Miller felt it necessary to take a swipe at two of the UK's leading actors who have more than proved their worth to undertake one of Shakespeare's greatest roles."