my bank, HSBC, told me a bankers draft only proves that the money is in the account when the cheque was written & there's nothing stopping the account being cleared the second after. I had the same dilemma with paying for a splitscreen camper recently, £34k!, the seller wanted cash and that wasn't gonna happen!
If you bank with the same bank it goes instantly. Most banks have a £10k limit though without a charge. HSBC don't have cashier service on a Saturday. I found someone I trust who banked with the same bank to transfer the money when I was with the seller and within a couple of mins it was in his account. It was Santander who have a much higher transfer limit.
I think I'd pay cash for upto £15k with a couple of handy mates with me or just arrange to meet outside a cop shop