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My guess would be no. Someone may know better, I think the sidewall will be too tall. I actually had a similar situation, my friend who is a mechanic ordered me 215/45/R18 instead of 215/35/R18 and they fit on the car, but it was by no means driveable. Good luck
If your suspension and wheel offset is stock then it'll be very snug. Any sort of lowering or aggressive offset wheels and you'll be rubbing massive. The MINI doesn't like tall tires at all! You'll be better off getting the correct tire size than dealing with what you ordered, sorry to be the bearer of bad news.
Even though it's only a 5% increase in height if your lowered there will be rubbing. Either on turns or with people in the back seats. You'd be better off just getting the right size. Depending on the tires you ordered they could be on your car for years.