That seems clear enough. However, this is one of those situations where a Bill of Sale, old maintenance invoices, old NCT certs and the stamped service booklet for the car as well as credit card or bank statements showing payments for routine servicing/maintenance present a powerful history of the car being in one person's sole beneficial ownership.It's shocking to me that someone in their 60's would have to go to these lengths to prove that they're not operating a business. Besides the fact that he bought the car 'as seen' 3 months prior to complaining and didn't have it inspected by a mechanic.
There are a few Bill of Sale templates available on the net. Even if the buyer refuses to sign a Bill of Sale, the vendor should read the document to the buyer and note on their own copy the buyer's refusal to sign or accept a copy, as appropriate.