From https://www.fasterpayments.org.uk/about-us/personal-transact... , the lowest Faster Payments limit I can find is GBP 10,000. GBP 25,000 is more common.

The technical limit for the system is GBP 1,000,000, and the lower limit is up to the bank to determine.

If I were selling a car in the UK, I'd ask for a bank transfer (e.g. laptop/mobile) and wait for it to confirm. If I wished to be especially careful, I'd meet the other person at their bank, and provide the cashier my bank details.