Like Slinkey says, the odds are that the brakes inside the 12" wheels will be 8.4" discs. Which is a good thing.

The way to check it is to google a mini parts website and have a look at what the discs and calipers look like. Have a look at both the 8.4" and 7.5" disc setups. If either lookslike what you saw through the 12" rims, you should be happy. If they don't, well, they're a conversion. Then you need to ask a lot more questions. But the odds are stacked in favour of the 8.4" discs - they were in Mokes, 1275LS's, English Minis post 84, etc. No dearer to maintain than S discs, in fact, generally a bit cheaper, as there were a good number of cars made in England with them - about 16 years of production (although they weren't Mini's biggest selling years by a long way). Probably the biggest reasons why people still install S discs (7.5" discs) are because they don't want to fork out for 12" wheels (which is why I'll be going that way, eventually) or because they want the 10" wheel look (it could be a genuine S, or a replica, perhaps trying to run without flares... the list goes on). In fact, in the UK, some people change back from the 8.4" to the 7.5" just to get that look.

But discs on a Mini is generally only a good thing. Many will tell you that the 7" Cooper discs aren't any better than drums, but, at the end of the day, even if they don't pull you up any quicker (which I'd debate!), you still don't have to adjust them after a hard drive. But the discs on the car you drove today are very unlikely to be 7" Cooper discs (which, incidentally, look pretty similar to the 7.5" discs you'll see on the websites).
I don't believe tyres are that much worse for a 12" rim than for a 10" rim - 13" tyres are the killer. There was a topic about it not long ago, might pay to try a search...
