I thought direct debits were guaranteed payment?
Thus the bill will be paid as normal, your bank account will go into an overdraft, and you will have to pay that back into your account when you get money, and pay a charge to the bank for going overdrawn.
Just happened to me.
I noticed I didn't have enough money in my halifax bank account to pay my O2 bill, but couldn't do anything cos it was a weekend. So once monday came along, checked my account, and the money had gone through to O2. I have a £1000 overdraft, but was already £990 into it, so when the direct debit was paid to O2, my account went over the limit, so I've got a £20 charge for that (which I'm going to try to get refunded).