The two men were leaders of the so-called modernizing wing of the party, and when Labour leader John Smith died in 1994, Blair and Brown were the leading candidates to succeed.
She said Blair felt some reluctance to seek to go first as party leader.
"He used to say in terms of ability that Gordon was way ahead of everyone and the irony is that if they'd only worked as closely together as originally agreed, his (Brown's) chance would have come sooner," she wrote.
One of the enduring stories of British politics is that the deal for Blair to go first was sealed at a meeting at a restaurant in north London.
Not so, Mrs. Blair says.
Discussions between the two men began very soon after Smith's death, she wrote, but she suggested that the deal was made at the home of her sister, Lyndsey Booth.
"It was always a given that they would work in tandem and that when Tony stood down Gordon would take over. Tony also made it clear to Gordon that he had no intention of staying leader forever and that when he did stand down he would support Gordon as his natural successor, assuming they worked well together ... in the meantime," she wrote.
"As far as I know the timing was never discussed but when Tony left for Lyndsey's, I made my position perfectly clear, even if I framed it as a joke. 'If you agree with Gordon that you're going to do this for one term only, don't come back home. Because that's just ridiculous,'" she wrote.

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