I always used to put my old car in early for its M.O.T.Although I was lucky to pass each time,the pass
certificate was dated to begin on the original date.This meant the old certificate was still valid during the interim period.
Hope this helps.
sorry to disagree with folks but with the new MOT system, the fact that a car has failed is logged on the computer system, so that would override the 'paper' certificate.
That is the risk of having an MOT test early, if it fails it is legally unroadworthy.