Stormbreaker (2000) by Anthony Horowitz. The book has a Prime Minister of the United Kingdom who hosts the grand opening of computers for schoolchildren. The book takes place in the year it was published; Blair was Prime Minister of the United Kingdom at the time.
Number Ten (2002) by Sue Townsend, in which British prime minister Edward Clare is based on Blair
In the Presence of Mine Enemies (2003) by Harry Turtledove. Charlie Lynton is almost certainly named for Anthony Charles Lynton Blair, Prime Minister of the United Kingdom at the time of the book's writing. Like Lynton, Blair was born in Edinburgh, but appears more English than Scottish in his speech and bearing. He was also born in the mid-1950s and became party leader in the mid-1990s. However, unlike Lynton, Blair is not a fascist.