PCD - Pitch Circle Diameter

I thought all minis have a 4 inch pcd (pitch circle diameter - the diameter of a circle drawn through the centre of the holes/studs). So measure as well as you can across the centre of two opposite, not adjacent, studs. Then do the same for the wheels, and see if they match.

Almost nothing else has 4" pcd - just Imps and Vauxhall Vivas and Firenzas and Morris Minors. Metros up to 1990 ish (the A series engine cars) had 4" pcd, but the wheels had different offset. The K- series metros seem to have 100mm PCD, so I suppose it is possible they changed the latest minis, but it seems odd they would do it now after all these years.

Lots of cars now have 100mm pcd which is close but not close enough - Rovers, Hondas, Vauxhalls, VW, etc. 4" is about 101.8 mm, and you can tell the difference from 100mm if you measure carefully. Fords and Peugeots are about 4.25"  PCD, I think.
Triumphs were 3.75". There were minilite type wheels on rear drive skodas - I think they were approx  5" or 125mm, and I don't think they fit anything else. Certainly not minis.

If the wheels and the studs are all 4" pcd, the wheels may still not fit, depending on the kind of brakes you have.

Wheels for drum and disk minis have different offsets, the hubs on disk minis stick out about an inch further, so the wheels have a deeper hole on the back, if you follow me. Put a straight edge across the inner wheel rim, and measure to the inner face of the wheel hub. That depth is usually about 4 inches on a 5" wide wheel designed for disks, about 3 inches if designed for drums. Metro wheels were too deep for minis - about 5" deep if I remember right.

If the car has drums, and the wheels are for disks, the tyres will foul on the shock absorbers, and you need to fit one inch wide spacers, and longer wheel studs all round. You will then probably find that your wheel bearings fail because the centre of the tread is not in line with the centre of the bearing, and drum cars have ball bearings instead of the stronger taper roller bearings on most disk cars. Personally I wouldn't do it.

If you have a drum car and disk wheels you could convert to disks, but you need AT LEAST the complete set for the front - calipers, drive flanges, swivel hubs (with the roller bearings) different drive shafts, hoses - and preferably the different brake pedal and master cylinder too. Also the rear drums, hubs, studs, bearings and wheel cylinders are different on cars born with disks. The drums have built-in one inch spacers, hence the different studs and bearings. Plenty people just change the stuff on the front corners and put spacers on the back, but I favour changing the whole system.

There is one other problem I have hit - I had big non-standard calipers on one of my cars, and some 12" wheels would go on, some would not go on, and some would appear to go on but when you tightened the nuts the wheel would not turn. Revolutions and Mistrals and Carmonas were OK, but none of the Austin Rover/BL alloy or steel wheels would fit on the front. This was due to the shape of the inside of the rim, and the position of the "well" that the bead slips down into when you are changing the tyre.