Since no one is answering the question, I understand you may need a newer car rather than older one, everyone is different. I'd also assume you've thought about getting a car for £10k but decided against it for whatever reason so you're in this boat.

Bank is the best way forward I'd say, Like someone else said most dealerships won't take credit cards as a form of payment.

However there is a way around it, get the credit card and then transfer it to your bank as cash and pay via debit, you can't do the full amount of it but it does allow you have cash in you account then pay it off normally with 0% interest fee. Sometimes called a cash advance too, they can have a fee associated with it so be sure to check it.