I'm a bit worried about having a runflat tire on one wheel and a non-runflat on the other wheel on the same axle, especially on the front axle under cornering as the stiff sidewall of the runflat would make it quite squirrely. (For this reason I'm not sure about the safety of using the space-saver spare with a runflat tire anyways.) I'd buy two new non-runflat tires if I were in that position.
If your Cooper didn't come with a spare tire, buying and fitting the kit for a spare is more expensive than buying a fifth full-sized wheel and tire. Having a matched wheel and tire would be best for safety. If you are going long distances that might be your best bet and one will even fit in the boot standing up (may have to lift the carpet on a Cooper and/or remove the cargo shelf). This is still safer than a standard non-runflat tire as you can change your wheel at a gas station rather than the side of the road.
Or of you're really worried, you can go Paris-Dakar rally-style and put 4 spare wheels/tires in the back seat
They fit fine as I know from getting my snow wheels put on in the fall.
Harry