Any chance of getting my money back?

I went to a Christmas fair today, it was lovely and we bought a few nice things.

At one of the stalls we tried to pay by card but the card reader apparently wasn’t working so we gave cash. However, I checked my bank balance on the way home and the money has in fact been taken from my account so I’ve paid twice.

Unfortunately it was a very informal market place and I didn’t get a receipt or any other proof of the transaction.

I have found that they have a website and have written to the company via a web form and am waiting to hear back. I know there is the option of raising a dispute with the bank if the company are uncooperative but I’m hoping not to have to go that way as they seemed really nice at the event.