The allegation was levelled by Lord McAlpine of West Green, the former Tory treasurer, who says in his latest book, Once a Jolly Bagman, that the donation was the highlight of his career as a fund-raiser and came a year after he had given up the job.
The delicacy of the issue was underlined by Labour's deputy leader, John Prescott, who wrote to Mr Major about his alleged involvement in raising party funds from foreigners. In an interview with The Independent, Lord McAlpine said Tony Blair had demonstrated leadership quality, but Mr Major had "shattered" his party.
While saying Mr Major was a good negotiator, he added: "I think in truth good negotiators don't make good prime ministers, because being prime minister isn't about negotiation, it's about leadership."
He also said he now favoured public disclosure of big donations. "If you ask me if I think that sums of pounds 10,000 or pounds 15,000 or pounds 20,000 should be private, then the answer's 'yes'. If you ask me whether a sum of pounds 5m should be private, then the answer's definitely 'no'."
In his book Lord McAlpine said that in 1991 he was asked to meet Mr Major at his Commons office, where he had been asked to "help them out" by approaching a generous donor, identified in yesterday's Scotsman extract from the book as John Latsis, a Greek shipping magnate, who gave Lord McAlpine a bearer's bond - a cash equivalent - for pounds 500,000.
Lord McAlpine did not look at the bond, put it in his pocket and went out to dinner. Next morning, as he walked across Hyde Park to get to party headquarters in Westminster, he took out the bond, saw the sum and caught a taxi. He said: "From this episode, there is no doubt John Major as Prime Minister has played a greater part in the acquiring of donations than is good for either him or the party itself."
Since then Mr Major has distanced himself from fund- raising, but Mr Prescott said in his letter: "The country needs to know if it is true that you asked Lord McAlpine to solicit a donation from John Latsis ... We need to know how many other foreign businessmen have been approached for donations to the Conservative Party at your insistence.
"And we must be assured that no hint has been given that policy might be affected by such donations."
Earlier, a Downing Street spokesman said he did not know if Lord McAlpine's allegations were true but insisted Mr Major had been "absolutely scrupulous". It is most unusual for the Prime Minister's office to get involved in party-political issues, and to talk about Mr Major's activities as leader of the Tory party, but the spokesman said: "It is the Prime Minister who has set down that there will be no question of any fund-raising taking place in Downing Street. [He] completely divorced himself from fund-raising activities ... The Prime Minister, since he became Prime Minister, has taken a very principled point of view about fund-raising."