From October, if you sell a used car, you're required to inform the DVLA that you no longer have responsibility for the vehicle. If you let them know, you'll get a full refund for any months remaining on the vehicle tax, but if you don't you could face a fine.
Failure to notify the DVLA about a change in ownership could leave motorists liable for speeding and parking fines for a car they no longer own. The best advice for sellers is to send the V5C document straight to the DVLA – don't presume the buyer will do it.
And if you buy a used car, any remaining vehicle tax won't be transferred, so you'll need to organise tax for your new vehicle before you get behind the wheel.