The best thing to do is head over to MINI Torque, and see what's out there. They can be a little intolerant, and swear a lot, so be warned. I reckon you'd need more like gbp4-5k for a decent facelift (2005-06) R53 with some fettling.
The major issues are all well documented and include power steering pump, coolant expansion tank/thermostat, leaks from rear boot handle, timing chain tensioners, failed front wishbone bushes, and engines that weep oil. Brakes are weak, and you really need to avoid run flats, and heavy OEM rims.
They are great fun, very robust, and - provided you're not on 18s, run flats, and old suspension, great fun to drive. They're easy to modify for more power: a reduction pulley on the supercharger is the trick.
I've had mine since 2008. It's still a work in progress...