Vets stating they cannot refund me £600

I took my cat for an emergency visit last night that ended up in an overnight stay. The vets stated I needed to pay £1200 upfront for the cost of all treatments. Long story short she ended up not needing half of what I paid for, so they stated they will refund me roughly £600.

I did not have £1200 in my bank account last night, so I stuck it on a credit card as I had no other option. Come to today, trying to get my refund, and they can’t due to it being a credit card so obviously no sort code and account number. They are saying they also cannot pay it any other card other than the one I paid with

Where do I go from here? My cat is insured, but I was trying to avoid going down that route. I also don’t know if they will pay out for treatment she didn’t receive that the vets should be refunding me.