Our registration number stays with the vehicle for the life of the vehicle (there are exceptions, you can pay to have a particular valid number, and can transfer that number to another vehicle, but that's not the norm) There is no requirement to change the physical plate.
The vehicle tax has to be renewed by the end of the month in which the current tax expires. When this is done, the authority checks that the vehicle is insured, and has a current MOT test certificate (if the vehicle is three years or older). This information is kept in a central database. The maximum period for the vehicle tax is one year, but you can tax it for six months except for small motorcycles.
Driving without tax, insurance, or MOT test certificate is immediately an offence, with the exception that you can drive a vehicle to an MOT test station without a test certificate or tax provided you have a previously arranged appointment and you have insurance. You can also drive it after the test back to the keeper's address provided that the test didn't show the vehicle as unroadworthy. You can never legally drive without insurance (though a significant proportion of drivers do).
Cost of the tax varies depending on type of vehicle and its emissions. Motorcycles range from £17 ($27.40) to £80 ($129) for a year (my FJR is £80 for a year, or £44 ($70.80) for six months). Cars vary between zero and £1080 ($1740). Cost of the MOT test again depends on the vehicle, for my FJR it would be £29.65 ($47.70), but it's only two and a bit months old, so no test needed for nearly three years. By that time the fee will have gone up, of course. (Maybe I'll be unable to ride then anyway due to my having aged yet another three years
.)
From this month onwards, the only check that a vehicle has its appropriate taxes and test certificates will be done on line, usually from an ANPR (Automatic Number Plate Recognition) camera. ANPR cameras are installed in police patrol vehicles, mobile road-side units, and possibly some fixed locations. Even the paper insurance certificate is not worth anything as far as validity is concerned. If you are stopped or investigated for any motoring offence, whether by a human or a camera, the police will check that you/your vehicle have valid insurance cover on line, or will check with your insurance company by phone if the on-line check fails.
Insurance requirements are that there must be insurance that covers one or more drivers for a particular vehicle. If that insurance doesn't cover another driver, (s)he must have separate insurance that allows him/her to drive the vehicle (not necessarily specific to that vehicle).
There is now no physical evidence on the vehicle that any of the legal requirements have been met.