Alex, under U.S. law, you have more protections in writing about public figures than about private ones. British libel laws are different (and often stricter) than ours.
But if the public/private figure laws are similar, I'd guess that Blair knew he could spend a fortune to sue Harris and lose (and that Harris has written enough books to know what he could get away with).
Much appreciate your mentioning this because plaintiffs, some authors or not, do "jurisdiction-shop" and sue in the country most favorable to their case. So you've given me a chance to say: What authors can get away with here may not be what they can get away with elsewhere.