There are three flying schools at Cranfield.
Azure Flight Training
Cranfield Flying School
L3 Harris
I don't think that Azure could do CPL or IR right now, although I'm aware they've just changed ownership and the new owner is trying to sort that out. I do like the attitude of the instructors there and the aeroplanes are well looked after.
L3 Harris are integrated, and you can find a lot of public discussion about their capabilities. The capability at Cranfield is large, but presumably they won't do a part time course.
I'm not personally a great fan of the attitude and aircraft management of CFS, and would be reluctant to use them myself. But, my experiences aren't recent, so they may be much better than my recollections. I would certainly encourage you to get recent experiences and visit yourself before making any decisions.
You might do worse than look at Booker Aviation at Wycombe Air Park for your wishlist, they're not that far away and do everything, with an excellent reputation. (Not been there myself for a couple of years, but heard nothing bad since.)
G