Contact the card issuer to get the charges 'charged back' to your account, they should give you advice how to do this.  As far as I am aware the same rules apply as to the credit cards which although they are to do with the credit protection legislation the banks make the same contractual rules apply to both credit and debit cards.

Card 'charge back' is part of the 'Merchant' agreement between the banks and the merchant that accepts the card payments.

You should also have protection by 'Trading Standards' if you are a private individual, contact your citizens advice for free advice on this.

You can also get simple redress through the County Court as a last resort and the court fee is refunded if the other side fails to defend and if you file against them then they would probably admit liability and pay into the court which would also include your court fee.  You need to write to their registered head office to warn them of your intentions if they do not give you a refund, tell them they have 14 working days to pay or you take court action.  Put it in writing, much better.  You can take action online:

www.hmcourts-service.gov.uk

court action is the last resort though but the small claims you don't need a solicitor and for such small claims it is unlikely they will defend.