When we lived in London I grew a plant of Tibouchina urvilleana outside, but sprawling up against a heated greenhouse. In that position it did tolerate the (very light) frosts we had. But it certainly wouldn't take significant frost. And it needs plenty of water.
It's a big genus and there may be some species from higher altitudes, but really they're all tropical or at best sub-tropical and I doubt if any are suited to Mediterranean conditions.