Heathrow is BA's base. However, they of course have a very large presence at both airports. Basically Heathrow is the bigger, newer, and more highly thought of of London's airports so it is naturally BA's base.
MEB is correct. I just wanted to add one quick thing. CityFlyer Express which is a subsidiary of BA is based at Gatwick and flies RJ-85-100's ATR-42's and ATR-72's from there. This adds alot to BA's presence at Gatwick.