Thanks all, and NZ_M3 particularly. Love that this kind of information is available from you guys.
There's a good news/bad news update to this story...
The good news is that the car is going back to Elms to get fixed, which means I don't have to live with the door seal hanging off and I don't have to try an amateur fix myself (which I would undoubtedly fuck up).
The bad news is that it's going back to Elms, only a week after having been there, because on my way to Cambridge to put the car into storage and after turning the stereo down, I noticed a loud and definite knocking noise from the top end of the engine which quickly became a cacophony under load. I didn't dare drive it further because it sounded pretty terminal.
RAC said they would take 90 minutes to send someone, so instead I hitched up my CSL to my wife's Megane RS (she was following me to drop the car off) and we towed CSL to Elms. There's one thing that won't endear you to a BMW sales guy, and that's arriving at their "Platinum" sales event in the middle of the day with a ton of punters on the forecourt and with a Renault towing BMW’s flagship sports car.
Anyway, more work for Gareth (thanks mate) and hopefully it's not so serious.