Thanks for your messages so far. It is comforting to know that my dd (only child) is not some kind of freak and that this is a common problem with many toddlers. Will check out the other makes mentioned.
Tesco works for us! We've always had this problem - My boys trousers always fall down -he's wearing 12-18 months and he's 2 and a half. They're elasticated all round and start at size 4 I think (maybe 3).