I think honesty is the best policy on this one. If they have specifically stated that they won't accept people without squeaky-clean credit my guess is that they'll do their homework and find out anyway.

Coming clean may be the best and only solution. It's better to know now that it isn't going to go through than the day before exchange of contracts. You might be able to pursuade them to accept you anyway, talk to them and explain why you got defaults etc and they could be more sympathetic.

If it's a no-go and they didn't explain the "good credit" clause before you put your money down, you should be entitled to your money back.

Good luck.