By law - no. If you ask your neighbour if he minds if you paint your side, it shouldn't be a problem, but you can't do it without his permission, because it is his fence, and in the eyes of the law, that includes your side of it.
Although have you checked the land registry just to be sure it is owned by him? It may well turn out to be your land! Although I don't suggest starting a legal battle purely for a painted fence ;)