The battery should read 12.6 volts. I've seen bad batteries at 12.2 volts. Not that this is your issue, but does your sons R56 have an IBS unit? I suggest you read up on this article here:
MINI Cooper R56 Battery and Connection Notes Replacement (2007-2011) | Pelican Parts DIY Maintenance Article. I also suggest you go to the bottom of that article and leave your comment there as well. Nick, our MINI guru will have additional input for you.