I would NOT do it. Dealer could go bust over night and I lot of what appears to be owned by a dealer and on their forecourt is often not the case. Paying by debit card should not be a problem. Also have you considered the consequences should you require and warranty work on the car

Never had to do this with any car I’ve bought. All the dealer needs is cleared funds before the car leaves, so a credit or debit card is absolutely fine. It may be their policy but it may be a way to make things more difficult to walk away if you turn up and the car isn’t right. I’d call and explain that you don’t want to pay the balance until you’ve seen the car in the metal, a card transaction will clear instantly and they can easily check the money is in their bank.

Money won't be in their bank from a card transaction. They'll have a card authorisation number but that's all.

I can sort of understand a dealer reluctant to take £15000 on a card. Firstly it will cost them and secondly there is a fraud risk (small, but there).

Proving your bank reliably makes faster payments for £15000 then a bank transfer whilst you are there is the best bet. That way dealer can be confident payment has been made as it will be in their account and you will have seen the car.

I've been at the other side of this, one of several car transporter drivers pulling up at a dealer at 8am ready to take away the entire stock of cars once the Receiver has sorted out which are going where.

Normal people like us hearing about the sudden failure arriving during the morning, some angry some in tears, having only the day or two before paid serious money in large deposits, don't know the legality if people had paid in full, an unpleasant but thankfully rare side of my previous work.

I too wouldn't be paying until i had the car in my grasp there and then, you don't know these people from a bar of soap.

If the dealer is asking for a credit card payment in advance, I wouldn't be too concerned. if they go bust, even if there is no car, you are protected up to £30k. If they're asking for a bank transfer, I wouldn't agree to that.

I'm not sure why they would want the money up front but perhaps they're sick of scammers and non-payers. Equally, the car might be a dog or they might be trying to get you on the hook. In these matters, I try not to concern myself too much with the why of the issue and rather concentrate on the risk to me. As I said, pay by credit card and there is (in any practical terms) no risk.

I remember reading advice from HJ years ago regarding an instant cash in hand payment (sort of), which should work well for both parties. IIRC, the buyer withdraws the amount in cash from their bank and immediately pays it into the seller's account as a cash payment in their presence, which should obviously be cleared with no possibility of cancellation. Ideally, seller and buyer have an account at the same bank.
I imagine it's all but impossible to do this nowadays as banks hardly hold any cash on their premises!