I haven't run across this one before, but my first thoughts are that as a private transaction between non-registered individuals, it doesn't actually matter that it was VAT-exempt when new. (I'm not an accountant or VAT expert).
VAT-registered UK 2nd-hand car dealers have VAT on the difference between their purchase price and selling price; their gross margin includes a 15% VAT element. Private individuals selling or buying 2nd-hand cars to / from other private individuals don't have to account for VAT.
Does your purchase price reflect the fact that the car was VAT exempt? It should be a bargain.
Was the car converted and has it been converted back?