Sorry pal, but that is complete and utter bolloc*s.
I wouldn't go near any MOT garage that said that - as they have obviously not read the latest/current VOSA Tester's Inspection Manual or the VOSA regular bulletins and updates.
VOSA had so many folks 'phone them about this that they actually issued a memo clarifying the situation.
Only petrol engined vehicles are subjected to a full cat and emmisions test and will fail if there was one fitted at the factory and it is missing.
Diesels only get a smoke test - the so-called 'cat' on a diesel is actually a particulate filter and is a different beast alltogether.
Get the VOSA downloads and read the truth.
Singvogel.