I believe this is the full text of the Google link which Barrow referred to in his initial post on this thread.
The way I read this - and I could be wrong - is that an owner could take a vehicle to an MOT station 3 weeks before its certificate expires. It fails on (say) a bald tyre but is then driven to a tyre depot to get it replaced. The owner could still then drive legally for those three weeks before having to have the vehicle retested.
No matter - it'll be irrelevant next month anyway.