No, M is for maintenance management. (Formerly known as the MMOE). 145 is for maintenance (MOE).
My CAP360 search was probably as enlightening as yours - but I'm amazed that part 2 is still available!
I suspect that "BCAR Section L" is more than a mere LWTR and may know more of this history than both of us!
My favourite trick to get out of using CAP360 (for police ops) was to ask the CAA for a copy...and when they could not supply one reject their insistance for complying with it!
I seem to remember that Part 1 was quite thin compared to CAP789...I'll see if I still have a copy of it. Dont hold your breath...
By the way; I think the EMA is going the right way (well, it was when I was watching them!) I left Marham as the MAA took hold and started to mess about with the MAP and Mil Regs - reverting (in my opinion) to their 'traditional' systems of work.
FYI, I was in military aviation for 24 years until 1999, but I was also working many weekends with my CAA LWTR for 10 years before I left. I've been in QA and AW positions for small and large operators since 1999.