I thought they did check for the noise level of the exhaust as part of the MOT.
I think the only fair way to test the noise would be at idle, because every car makes more noise when it's revved.
You shouldn't need to get an new MOT, I lent my old Mk3 16v to a mate who got pulled over on the M1 for having a rear light out. So he got a producer and I had to go with him to the local Police station with the current MOT to prove that it was still road legal. Didn't need to get a new one.
Your MOT cert covers you for 1 year, that should be end of story.
I got pulled in the same car a few months before this for a random roadside Police check, they checked lights, tyres and even emmissions, but not noise levels.
I'm always seeing Polish and Latvian cars in London, it's very annoying because they can't see properly (being left hand drive) and make bad manouvers, and most likely won't have had an MOT or even insurance cover for this country. I try to steer clear of them.