Only recently did Cameron come under fire for essentially prioritizing his constituencies needs before others. Well, I say prioritizing, for bringing his constituencies needs to the top of the list where he wouldn't have done that to another constituency.
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In America, you have the the legislature (The House & Senate.. equivalent to MPs although the house is based off population & senate is 2 members per state) and then you have the executive (president) completely separate. He/she is elected via electoral college.
A large part of constituency work is about getting bureaucrats to take notice of the concerns of little people. Even if the PM doesn't take the surgery, the letters go out on House of Commons (not No 10) notepaper over Cameron's signature. Few bureaucrats have so little interest in their own careers that they fail to take note of what the PM is saying.
Moreover when a PM cannot attend a constituency event, he has the "pull" to get a first-rate stand-in.