I've been thinking about this whole thing for a while and I've realised that MP's dont need to leave their constituencies at all. Videoconferencing technology is more than adequate to allow them to 'work' (or whatever it is they do to pass the time). And for the times they do need to arrive have a generic residence style building somewhere capable of accomodating all member of the house of commons.
Also with the exception of the prime minister MP's should not be allowed into the cabinet. Gordo talked about a cabinet of skills when he first came in and taken to its logical conclusion he's right. Advertise the cabinet positions and recruit them as you would any high end job going through an independant agency, making sure that you have candidates with the relevant knowledge and experience. Former teachers for education, doctors/matrons for the health service, former servicement (ideally who have seen combat) for defence etc.