Parking Fees paid to Premier Parking

I used a car park at Exeter Sandy Park for a 3.5 hour parking whilst at a conference. I made a mistake and paid for 2 days parking at £18.50 using a debit card. I contacted the staff at the conference centre who said parking wasn't anything to do with them. They said I needed to write to the card parking company Premier Park Ltd to obtain a refund.

The car park has CCTV tracking the cars entering and leaving to issue parking charges for anyone who is staying over there time slots. I called the company leaving a voice message on the answer phone recording my leaving time at 19.15 and arrival time at 16.00 stating I would be writing to them to request a refund.

I wrote a letter and had a reply saying due to human error no refunds can be issued, and I should check the transaction value before confirming.

I don't agree with this and think in the nature of fairness a refund should be given for purchases made in error. Is there any consumer law I can use to pursue my quest for a refund for the parking charges I have over paid. Or is a Visa chargeback my best option?

I've looked online at the Premier Park Ltd accounts and as of 31.03.16 they had cash of £314,506 and reserves of £555,998. I dont think they will miss the £16.50 overpayment I am trying to recover from them.