I agree with the "your body stops working" line as being the most basic answer that you need give. As for why it happens, I'd probably say "when you get very, very old", even though that's not necessarily true - I think for a kid of that age, even being 10 years old is so far away that they can't imagine, let alone nearly 100 years old. Btw, you've probably dealt with this part already, but having done some research a while back, I read that the best way to explain death was as the absence of familiar life functions eg. if a dog dies then you say it means the dog can't bark, can't chase sticks, can't run etc.
Penguinmum, I have exactly the same dilemma as you! The heaven idea is a very comforting one to a child, but as I don't believe in it I'd feel like I'm lying to my daughter. I've answered that question with a "people believe lots of different things about what happens after you die, and it will be up to you to decide what you think happens when you are older" - she seemed happy with that.