MPs do represent their constituents. But most do so via a Party platform. Actually that might be a bit naive on my part as in the past some have just followed their own, or some other, agenda!
Day to day they deal with constituent matters but in the bigger national and international matters only a united Party with several hundred voters all agreeing which way they're going can influence the outcome. Thus the Party platforms.
Of course, sometimes there is a free vote in Parliament where the issue is a moral/religious one.
As I said, people who do not want to side with others in a Party (to all vote together to achieve a particular policy) can stand as independents.