Cathy, you have an old Z-car? You must chat with mr.bill who is also a MINI2 member with a Z-car of similar vintage. And, like you, mr.bill is concerned about all the whiz-bang goodies on cars like the MINI.
But back to your original question. Unlike with some cars, Corvettes for example, MINIs don't use radio pressure monitors placed inside each wheel. Instead, on a MINI, the ABS system checks the rotational speed of each wheel as part of its normal functioning to ensure a wheel is not skidding. A side benefit of this is that if one tire looses air pressure it will rotate at a slightly different rate from the other three. By noticing this small difference, the MINI knows of a low air pressure or flat tire situation.