Don't know about a refund. But this is what I got from my bank. You cannot cancel payments if they are made from your Debit card. You have to cancel it with the supplier and hope that they won't take any more money from your account. Alternatively, of course, the best way is to call your bank and tell them you have lost your card and can they issue you with a new one. That way if anyone tries to take a payment from your debit card it won't be done.