Blunkett’s preferred job would be as chancellor, a post to which he has aspired under Tony Blair. He has no appetite for the position of foreign secretary because of the pressure of travelling.

But it is more likely that he will be offered a job such as leader of the Commons or chairman of the Labour party.

The minister, who returned to the cabinet in May as pensions secretary after his resignation as home secretary last year following the “nannygate” visa row, has patched up his feud with Brown; he has twice stayed at his home in Kirkcaldy, Fife.

The disclosures are in an updated edition of Stephen Pollard’s biography of Blunkett. Before he left office in December, Blunkett came under pressure over comments he had made to Pollard about cabinet ministers, including Brown.

In the first edition of the book, Blunkett said Blair “doesn’t like people who stand up to him”, in contrast to the chancellor, who “only respects people who stand up to him”.

He told Pollard that Ann Taylor, the former chief whip, was sacked because of her “inept way” of telling Blair what to do or say; and that John Prescott’s “two Jags” nickname “obviously gets to him”. Blunkett was also said to have referred to Brown’s allies as “little bits of slime from under stones”.

The comments earned rebukes from Prescott — who said they betrayed an “element of personal arrogance” — and from a Downing Street spokesman, who called them “unfortunate”.

Blunkett also believed there was a Brown “plot” to destabilise him over his push for compulsory identity cards.

Pollard now claims that all this changed after Brown gave Blunkett his “strong backing” when news of his affair with Kimberly Quinn leaked out in August last year.

“Brown rang Blunkett immediately on hearing the news to offer his support,” writes Pollard. “For all the cynicism usually (and often rightly) attached to politicians’ motives, it seems clear that Brown was genuine in his feelings for a colleague who was apparently guilty of little else beyond falling in love with the wrong woman.

“But there was also a more political side to his support. Just as relations between the two had been fine when Blunkett was not, as education secretary, a rival for the leadership, so Brown could see immediately that Blunkett had been wounded by the story and thus was less of a rival.”

Pollard adds that relations between the two men improved markedly after Blunkett’s resignation, when Brown no longer saw him as a rival. Soon afterwards, Blunkett was invited to stay with the Browns.

Pollard continues: “As work and pensions secretary, Blunkett has a major job once again. But his leadership ambitions are now at an end, and he and Brown are thus likely to enjoy much better ministerial relations than for many a year.”

But for his unforeseen departure last year, Pollard believes Blunkett would like to have have been made chancellor in the post-election reshuffle.

He is now being tipped for a possible return to the post of home secretary if Blair carries out another reshuffle before Christmas. This is unlikely until after Blunkett has overseen pension reforms.

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