Miss Dunaway, 53, was to have taken over the lead role of Norma Desmond from Glenn Close, who is preparing to open the show on Broadway in November.
But Sir Andrew announced on Thursday that he would rather close the show than let Miss Dunaway appear. Despite training he felt the actress, who does not have a strong musical background, would be unable to cope with the part.
His production company, the Really Useful Co, said in a statement: 'It was concluded after several weeks of rehearsals and vocal preparation that the musical demands of the role were such that it was not possible for her to perform as scheduled.'
Miss Dunaway and her managers said they were flabbergasted. 'From the moment I learned of (Sir Andrew's) decision, I thought, quite simply, 'this is yet another capricious act by a capricious man',' she said on the set of her new film, Don Juan DeMarco and the Centerfold.
'As to the question of my singing, which has been raised as an issue, from the beginning Mr Lloyd Webber told me he wanted an actress who could sing. . . When I auditioned for Mr Lloyd Webber I sang my range.'
She said that Sir Andrew had cast her in one vocal range, but later tried to push her into a higher one. She added that she would take legal action but declined to specify what the grounds for her claim would be.
Sunset Boulevard received grudging acclaim from British critics who normally dislike Sir Andrew's work. But the show has been dogged with bitterness about who should play the female lead.
The original production, based on Billy Wilder's great 1950 film about the claustrophobic and sinister world of Norma Desmond, a fading silent movie star, opened at the Adelphi Theatre, London and starred Patti LuPone.
She was to have taken the role of Desmond to Broadway. But Sir Andrew terminated her contract after Glenn Close opened in Los Angeles to ecstatic reviews from the American press.
He reportedly paid Miss LuPone about pounds 1m so Miss Close could transfer from Los Angeles to New York in her place.
Miss LuPone said the decision had left her feeling devastated. Sir Andrew said that he had wanted her to go to Broadway, but his American backers had insisted that Glenn Close get the part.
The Los Angeles production has taken more than dollars 25m ( pounds 16m) in ticket sales since opening last December at the Shubert Theatre. Advance sales for the production starring Dunaway had reached dollars 4m, which will now be refunded.