It is pointing to a battery/alternator problem or a connection problem.
My 2005 Cooper S cabriolet had exactly the same 2 weeks ago. RAC suspected alternator which I had replaced. Coming back from Gary Numan Concert in London last night, the steering goes heavy, battery indicator on. I started the journey back home to get as close as I could. After about 5 miles, I stopped at traffic lights and noticed that the battery light had gone out. When the lights turned green, I pulled away and the steering was back to normally assisted. The light then flicked on again for a few seconds and then off. It stayed off for 20 miles or so of bumpy London Roads and then highway at speed, and then came on again all of a sudden. I had to conserve battery power by turning off headlights when no other cars nearby. When I was about 3 miles from home, all the warning lights came on - ABS, airbags etc. and then all the dashboard and headlights went out. Fortunately I made it home before all power gave out.
So, for me it was not the battery (which is fine) and it was obviously not the alternator as a new one has made no difference.
Testing the voltage with engine running shows no increase in voltage though so in my case I suspect some dodgy connection or maybe a problem with the computer (hope not).
If anybody has ideas what my problem could be - please let me know thanks.