Everyone can and does make mistakes in some way or other. Common decency would obligate most people to return what is not rightfully theirs, however a good number of people fail to meat this criteria. I think you will find that an overpayment regardless of fault in the eyes of the law is an overpayment and since it is illegal to charge for goods or service not supplied, the landlord would be committing an offence under the Supply of Goods and Services Act. Rent is seen as a charge for the service of providing property for the use of the tenant, as such if you are no longer the tenant, the service cannot be charged for.

You will have a very good chance of making a case in law, as I mentioned before, this does not necessarily mean you would get the money back, but don’t give in, it’s your money, not the landlords, best of luck.