I used to have a Cooper R57 and there didn't seem to be any reason why the spacesaver wheel mounting under the boot floor couldn't be used. But I never tried it and haven't read of anyone else doing it. Correction: I've seen someone on an American forum who has done it.
If you have a Cooper S, then you definitely can't mount a spare under the floor since the exhaust is in the way. But if you have a Cooper (or D), it should work. The only way to find out is to look carefully at the good pictorial guide to fitting the spare wheel carrier that is floating around the forums somewhere. It goes into some detail, so you should be able to lie under your car and double check that everything can be fitted.