The AA guy said he suspects something "sucks a lot" from the 12V battery and that's why it's dead. He charged it minimally to park the car correctly at home.
so with my limited understand of batteries, either this :
1. 12V 20ah AGM battery is simply dead and all's required is replacing it, in which case I found this
https://www.sytnerstevenagebmwparts...al-BMW-AGM-battery/132287830/61219321815.html
2. or there's a fundamental problem and even if I replace it with a new one, it'll go dead again and I haven't solved anything.
The BMW Dealer here in South London charging £250 for the investigation.
so probably something like £500 for this "jump pack", to rent it from some company to get my car to the dealer in south London + £250 for investigation + £100 for the actually battery?
Alternatively, I can do DIY here at home after getting the battery delivered to me here? and I can explore youtube
Thanks for your help