Behind the disagreement is the Royal Shakespeare Company's simmering resentment that the Arts Council chairman, Gerry Robinson, has praised the National Theatre and given it a huge uplift in grant, while giving the RSC much less.
Yesterday, a senior figure in the Royal Shakespeare Company, associate director Michael Attenborough, said that the National Theatre had not had any successes with Shakespeare productions on its main stages.
And next week RSC artistic director Adrian Noble will tell Mr Robinson that his company has not only delivered artistically; it has acted in line with the Labour Party and government policy of taking theatre to new audiences, and particularly to young people.
The RSC's grant has increased by only 5 per cent to pounds 8.8m, while the National has received a 9 per cent increase of pounds 1m, which will take its Arts Council grant to pounds 12.2m. When he announced the grants recently, Mr Robinson painted the two companies in very different lights.
He said: "The RSC has problems. It needs help. Their problems are substantial and not even an increase of 10 per cent would have been enough to sort them out. It has taken on too much."
By contrast, he said of the National: "The National Theatre has coped brilliantly with standstill funding for the past five years, and the quality of its work and success at attracting new audiences argued strongly for a an increase of this kind."
Launching his new season yesterday, Adrian Noble pointedly stressed that the RSC had acted in accordance with Labour Party policy by moving out of London for half of the year and taking its work around the country. He also pointed out that the National runs three theatres in its building on the South Bank in London while the RSC has three in Stratford-upon- Avon and two at the Barbican Centre in the capital, as well as having residencies in Newcastle and Plymouth.
He said: "We have taken our productions to the regions. And 40,000 people have come to Stratford for the first time this year. Many of these have been young people."
An RSC insider added: "It's not so much the difference in money that's the problem. It's the National being lauded like that."
And as the RSC announced details of their new season yesterday, Mr Attenborough made a point of saying: "The National has not had a single successful production of Shakespeare on its main stages in the last 10 years."
That will sting the National, which has put on King Lear, A Midsummer Night's Dream, Richard III, Antony And Cleopatra, Hamlet and Macbeth in its main auditoria.
Mr Attenborough later qualified his statement by agreeing that Deborah Warner's production of King Lear and Ian McKellen in Richard III had had some success, though mixed reviews. But he said that only the RSC really knew how to produce Shakespeare on large stages in front of big audiences.
One senior RSC insider said that when the National had a critical flop last year with Helen Mirren and Alan Rickman in Antony and Cleopatra, "a lot of us in Stratford were saying to each other `now they know it's not that easy'."
The RSC yesterday announced one of their starriest years for a long time, of which one of the highlights will be Antony and Cleopatra starring Alan Bates and Frances de la Tour. The newly knighted Nigel Hawthorne will star in King Lear, directed by Japan's Yukio Ninagawa (a co-production with West End producer Thelma Holt); the first RSC production of Othello for 14 years will place black actor Ray Fearon in the title role, and Timon of Athens will play in the main house for the first time since 1965. There will also be an adaptation of Ted Hughes's Tales Of Ovid. The late poet laureate was working on this with RSC staff just days before his death.
The National will also be staging a Ted Hughes adaptation, his version of the Oresteia.
Adrian Noble said he would be meeting Mr Robinson next week and would be hoping to have the RSC's grant increased by special "stabilisation funding". This is lottery money earmarked to help companies restructure their administrative set-up.
A spokeswoman for the National Theatre retorted last night: "We have mounted a number of extremely successful Shakespeare productions on our main stages.
"When Othello transferred to a main stage from the Cottesloe it sold out." The Pay's The Thing: National Theatre. Artistic Director: Trevor Nunn Grant 1999: pounds 12.2m Olivier Awards 1998: six Staff: 650, including 170 actors Number of theatres: three Big hits last year: Oklahoma!; Tennessee Willams's Not about Nightingales; Michael Frayn's Copenhagen. Big plans this year: The Oresteia; Troilus and Cressida, directed by Trevor Nunn in the main Olivier Theatre.
Royal Shakespeare Company. Artistic Director: Adrian Noble
Grant 1999: pounds 8.8m Olivier Awards 1998: none Staff: 750, including 100 actors Theatres: five Big hits last year: The Lion, the Witch and the Wardrobe; School for Scandal; Hamlet. Big plans this year: King Lear (Nigel Hawthorne) Antony and Cleopatra (Alan Bates, Frances de la Tour).