My guess is that the battery issue is down to the BMW electrical system/canbus etc. It appears to be doctored a little to suit the Morgan and so has a lot of unused circuits like traction control etc.
Perhaps it creates a drain somewhere that is hard to identify. If ever you leave your key in the ignition (turned off) by mistake, within half hour the battery will be drained enough to prevent starting. I guess that might be down to some kind of immobiliser as well.
Whatever it is, it can be very frustrating!
Definitely something wrong with the car Shooter. Many cars with immobilisers / alarms / trackers have a small drain which flattens the battery in 2 weeks or so. Happens to the Fezza and also to my bike. But thats a drain of a few milliamps. What you are talking of, if you really do mean half an hour, is a drain of 25 amps or more. Thats not unused circuits! Whats more something somewhere would be getting pretty hot and maybe even smokey.
Much more likely is that you battery is duff. Batteries lose capacity as the powder falls off the plates and this is something that happens much quicker with heat and vibration. So its quite possible that a battery that starts at 60aH ends up at 10aH but will still just start the engine if fully charged.
Then of course there is the possibility of bad connections in the run to the starter. Bad earth maybe.
Either way if that half hour is literally correct then it needs proper investigation. I suppose it could be a safety program in the immobiliser that says " if the plonker owner has left his key in the ignition, we maybe should help him by immobilising the engine. Ja - ist gut!" Or something like that