This is what cargurus.co.uk say on VAT on second-hand cars…
If you are buying a used car in a private sale, there is no VAT to pay. If you are buying a used car from a dealer, then he or she will need to pay VAT on any profit made. This is known as the second-hand margin scheme. However, the amount of VAT will not be itemised on the invoice and is of no concern to the buyer. …
Pay attention to the line “However, the amount of VAT will not be itemised on the invoice and is of no concern to the buyer.”
Now you know why Arthur Daley was a car dealer.?