Trading Standards monitor used car ads and can/will take PT traders pretending to be private sellers to court. You can't hide your trading history to deny a customer the rights they are entitled to under consumer law, and the cost of meeting those obligations is something that a legitimate business just has to swallow.

Also, the taxman has a dim view of people trading in any field but not registered for them to get their cut.

If you were to try and deny being a trader but reliant on a Traders policy, I'd guess they could use that info against you.