The director has been angered by what he claims is an "outrageous" move to stop him bringing the production to London's West End for a 50th-anniversary run in order to protect the Barbican's own box-office takings - a decision he said would have "appalled" Beckett.
But the Barbican's boss, Sir John Tusa, has accused him of deliberately whipping up controversy and acting with a lack of respect to all involved. He is also accused of "bullying" the theatre because there had been a number of opportunities to stage the show earlier this year.
Waiting for Godot, a play where, famously, nothing happens, is widely regarded as one of the 20th century's most important theatrical works. It launched Sir Peter's stellar career after he staged the first English-language production at London's Arts Theatre half a century ago. He had aimed to bring his latest incarnation of the show back to the same theatre to celebrate the anniversary.
But the Barbican and its partner, the Gate Theatre in Dublin, blocked the move because they are staging their own versions to coincide with Beckett's centenary early next year. The rights to all of Beckett's works have been granted jointly to the venues, allowing them to veto other productions.
It is common practice within the theatre industry to protect the rights to a play to prevent numerous productions being staged simultaneously or within a few months of each other.
Sir Peter said: "I'm very upset about it. They have refused to allow us to do it in September because they say it will upset their box office. It is outrageous. The Arts Theatre only holds 320 people so it is hardly major competition. They wouldn't even have a meeting to discuss it.
"John Tusa wrote me a letter back saying he hoped we should shut up about it or the world would see it as a silly 'luvvie' spat. So here it is - a silly luvvie spat.
"Beckett would have been appalled," said the director, who is rehearsing for a short run of Godot at the Theatre Royal in Bath that begins on 16 August.
But Michael Colgan, director of the Gate Theatre, hit back at Sir Peter, saying he was distorting the situation.
"He's coming on like a child with big tears coming out of his eyes, saying 'this is terrible, nothing is happening' - but what is happening is that he is trying to bully us."
Mr Colgan said he met Sir Peter last year and was told about his plans for a London run. Far from being treated ungraciously, he said he was given an opportunity to stage the production in the first half of this year and that was then extended to 1 September.
But Mr Colgan said it had become like "grandmother's footsteps", pushing back the date until closer and closer to the Barbican's run and a line had to be drawn.
"[Beckett's] estate do not want two productions on at the same time. You can't just say I did the first production so I should be able to do it."
Sir Peter is now seeking to stage a one-off performance of Godot at the Arts Theatre on 4 September, when the Bath run draws to a close.Reuse content