A car towing a caravan/ trailer should display a number plate at the front and the vehicle behind will have the same number plate on the back, so 2 different vehicles same number.
Interesting question - the law states that the vehicle MUST carry its registration number on a plate but doesn't state that you can't have any other plates on. The registration plate MUST be lit (at night), so a second plate, not lit, could be classed as not the registration plate. In addition many lorries have plates on carrying the firm's identity number eg, Eddie Stobart lorries might carry ED1, ED2 etc on plates which could be registered to other vehicles.