The accusations are made in a letter to the London Evening Standard, for which he works, from 35 artists, art historians, curators, dealers, writers and fellow critics.
The letter, published yesterday, pulled no punches and showed that Mr Sewell's sharp writing style and wicked sense of humour have made him many enemies in the London arts world.
However, Mr Sewell was unrepentant last night and said he had no intention of replying to his critics. He added: 'My reaction to the letter is to get an acute fit of the giggles.'
The letter said: 'We take the greatest exception to Brian Sewell's writing in your paper. His virulent homophobia and misogyny are deeply offensive.
'. . . Although very occasionally he says something perceptive on subjects where he has some expertise, he is deeply hostile to and ignorant about contemporary art.
'In place of an informed critique, week in and week out he serves up the same tedious menu of formulaic insults and predictable scurrility - the easiest and cheapest form of demagogy.
'. . . We believe that the capital deserves better than Sewell's dire mix of sexual and class hypocrisy, intellectual posturing and class prejudice.'
Among the signatories are Professor Christopher Frayling, head of the cultural history department at the Royal College of Art, George Melly, the jazz musician, Sir Eduardo Paolozzi, the sculptor, and Rachel Whiteread, the artist and winner of the 1993 Turner Prize.
It is not the first time Mr Sewell has been accused of being prejudiced against women. Last year he was alleged to have banned female contributors from a Channel 4 television programme which he was recording.
Mr Sewell replied yesterday: 'I take the view that feminism is nonsense and I am therefore being accused of being a misogynist. It is not true.'
The accusation of homophobia was also rejected by Mr Sewell, who was a close friend of the late Anthony Blunt, the homosexual spy who was an art historian and Surveyor of the Queen's Pictures. Mr Sewell said: 'Nobody should be given privileges because he is a homosexual. There is a homosexual Mafia in the arts world.'
He said that his column in today's Evening Standard would probably make him more enemies, although he will not allude directly to the criticisms. He added: 'My column is too serious to be used for such trivia.'
Mr Sewell's critics say they want him to take a more constructive attitude towards the arts in the capital and not to breach what one yesterday called 'the bounds of reasonable criticism'.
They are unlikely to get their way. Stewart Steven, editor of the Evening Standard, said yesterday: 'Brian Sewell's contribution to art criticism in this country is immense, as artists of genuine talent acknowledge. Painters who can paint have never had anything to fear from his pen.'