Mr Baker, the former ally of Edward Heath who became one of the two last-ditch supporters of Mrs Thatcher's continued premiership, claims that Mr Major was 'literally silent' during the Thatcher campaign. The allegations are published in today's Sunday Times, which is serialising Mr Baker's memoirs.
And he says that Mr Major even hesitated when asked by Mrs Thatcher herself to sign her nomination papers to go forward for the second of the two ballots, in November 1990.
Mr Baker says that he urged Mrs Thatcher against travelling to Paris for a summit meeting during the first ballot. Many of Mrs Thatcher's most fervent supporters said that the decision to go ahead with the Paris trip cost her the premiership.
When three of her closest supporters telephoned Mr Major - who was recovering from a dental operation - to ask him to appear on television in her support, he said: 'I'll have to think about it.' By the time he returned to London the following day she had resigned.
Mr Baker also says that when earlier she personally asked Mr Major to sign the second ballot forms there was a 'long pause' before he replied: 'If that's what you want me to do, I'll do it.'
Although the implication is that Mr Major did not strive to keep Mrs Thatcher politically alive, he can point out with justice that many of his colleagues - across the party spectrum - told her bluntly that they did not think she could win against the challenge by Michael Heseltine.