MOT Enquiry

You're good to keep going on your previous MOT, the failure for the tyre does not cancel the earlier test certificate, the car should not be driven with a dangerous defect however until the problems been rectified.

This area of concern between mot certificates still in force and new mot fail over lapping the old pass certificate should be looked at in more detail and put some type of clarification on the mot history page of customers vehicles to advise them accordingly. A legal definitive guide.

If the constabulary pulled you over as a routine check and found that you had been driving a vehicle with a fail document in force, even though the previous mot certificate is still in force, the constable to cover his own back may very well report the incident. Let's try and be fair here, the constable might not be a technically trained person.  

Having said that, google mot history check for your vehicle and see of the fail document is recorded!

The reason I advise this is because a recently tested vehicle by me still had an old certificate in force, and although the new fail overruled the old pass certificate, the new fail actually did not show on mot history! Was this an overlap period or is this something DVSA have done when an old test certificate is still in force?

That is how I understand it too Wally. Driving with a valid MOT and no Known faults is not a problem.