The system is fully integrated now. In the past you used to get policemen standing at traffic lights after the end of the month, checking for out of date tax discs.
These days all polices forces and the DVLA have ANPR(Automatic Number Plate Recognition) vehicles and carry out regular scanning of major roads. Tax, Insurance, and MOT are all automatically updated on the DVLA system when they are renewed, and this information is automatically checked by the ANPR vans within seconds of the vehicle passing.
Most of you have probably seen these vans sitting on bridges above motorways and trunk roads thinking they are speed camera vans. The clue that they are ANPR is that you will usually see police cars in the next two or three lay-bys or side roads , who are informed within seconds if a non compliant vehicle has passed the ANPR cameras, they then follow them and stop them up the road and take whatever action is required.
The tax disc is now a bit of an anachronism, and I would think it unlikely you would be done if you didn't have one visible. Even policeman on foot can get the DVLA information within seconds if they need to. I think within a few years the Tax disc itself will disappear.
Until a few years ago if you had the vehicle off the road for repairs etc, as long as it was actually off the public road and on private property no action was required by you. It is now necessary to fill in a SORN( Statutory Off The Road Notice) form if you do not renew your tax, which can be found on the tax renewal form you are sent from DVLA.
