Searchlight seems to have answered his/her own question. As long as the bank account continues to exist (with funds in it) and the creditor declines to cancel the continuous payment authority, his/her bank is obliged to continue making the payments. Closing the account is the only possible option.
However it's possible that, when the bank receives the next call upon funds in the 'closed' account they might still honour the payment and tell Searchlight that they regard the account as still active but overdrawn, resulting in some hefty charges for Searchlight. (That's what they would do if, for example, someone presented a cheque - backed by a cheque guarantee card - drawn on the 'closed' account). So the account should not be closed until Searchlight has sought clarification of the matter from his/her bank.
Reference:
http://www.financial-...utomatic-payments.htm
Chris