As long as it's 12v and it has an alternator, it will work.
But for how long? Not long, and not well. Odds are, if you keep the stock battery and alt. the headlights will flicker when you're listening to music. Sometimes they'll turn off. Your gauges will go haywire at any time, and you can no longer listen to the radio when you're car is not running, as the battery will die very quickly.
I do battery upgrades and new alternators about 50% of the time when I do installs for clients. It's not incredibly hard, but on a mini, it could be a tight squeeze to get the alt. off. Battery may have to be relocated to the trunk/boot if you can't fit a bigger one.
Too bad you're not nearby, it seems you live across the pond. I do all my installs for:
Parts Cost +10% of parts, and $20 an hour labor. Pretty reasonable.