This is an early and very thorough biography of Spencer (dating from 1991). It covers his life from an examination of his paintings (a method not to everyone's tastes).
I would suggest that since most of the illustrations are black and white, that looking at another biography first would be a good idea if you don't know his paintings that well. The Kitty Hauser biography, in the British Artist series, is more accessible and quite short. The Fiona McCarthy biography is more recent, very thorough and perhaps a better alternative.