Taken twice by Direct Debit - yes under the Direct Debit Guarantee, via your bank.
Direct Debit taken after you paid the bill by another method - no. When you paid by the alternate method you would have been warned that the DD would also be taken. The additional payment becomes a credit on your account and will be used to pay your next bill.
I can see that it has been awhile since you initially posted about this. Are you still experiencing this issue or have you either contacted us through other methods for support or managed to follow the advice of Ernie_C?