What year and model is your car? The first gens use an indirect TPMS while the second gens use a direct TPMS (tire pressure monitoring system). Bottom line, no, unless the tires are under-inflated or different sizes.
To know just how to advise you, the year and/or R## of your MINI is needed, i.e. rotation sensors or pressure sensors. If you have rotation sensors, tires of different types could cause it to throw an error. Stand by for the tire guru to jump in on this.
