Best and cheapest way to transfer funds from UK to Panama

Do you have a bank in Panama? Transfer money from your UK bank to it.
You can use your credit/debit card from your UK bank to get cash from an ATM here, but I think you’re u’re limited to $500/day.
I’ve transferred money directly to a Panamanian’s account but I don’t know if that works internationally.
Ask the seller for ideas? If it’s a dealership maybe they take VISA or other credit cards.

Cash.  Hand-carry up to 9500 USD in cash (per person) from UK bank (with withdrawal slip) on airplane.  You're making the trip anyways.  You get a decent exchange rate for your GBP to USD.

Otherwise, you're going to have to wade through verification for AML/KYC compliance as required under Basel III rules:

Bank Wire. You are going to get screwed with an administration fee on the UK end, on the Panama end and they will take a small percentage cut.

Western Union:  They will take up to 15% as commission.

Credit Cards: you're going to be charged around 5% 'convenience fee' to cover the fee charged by the credit card operator and the bank; expect a delay while they review the transaction and another delay while they pay the dealer.

There are some smaller programs that prefer personal invitations.  I'd have to send you to them personally.  Feel free to contact me through messaging.