The challenge I have is trying to establish whether I need to get the EASA SE Single Crew endorsement and if so, where from or does it form part of the course at Tarbes.
No you don't need to get a SE single crew endorsement - that doesn't even exist!
If you have done the TBM 850 class-rating (it is a class, not a type) and if you hold IR/SE Single-Pilot, then you can fly the TBM850 single-pilot.
The same applies to other EASA aircraft which can be flown single-pilot (eg C510, C525, PC12). All you need is the class-rating and single-pilot IR.