Vehicle Excise and Registration Act 1994
31A Offence by registered keeper where vehicle unlicensed
(1) If a vehicle registered under this Act is unlicensed, the person in whose name the vehicle is registered is guilty of an offence.
So both registered keeper + Driver (if not same) are guilty of the offence. (Like allowing somebody un-insured to drive awards you points)
They can indeed, the DVLA have cars with camera's (Example) specifically checking tax.