No. MPs are elected as representatives, not delegates. That is to say, their job is to represent their constituents' interests: they are not there as proxy voters for their constituents opinions.
It is not unknown for constituents' interests to be in conflict with those constituents' opinions of what should be done: after all, virtually none of them are specialists in the causes and effects in question, nor do they have access to expert advice on those causes and effects.
The UK is almost exclusively a representative democracy, rather than a direct or participatory democracy. Its referendums are rare and dysfunctional.
There are parliamentary customs that make it easier for the government to carry out policies that were in its election manifesto. But the manifesto does not bind MPs.
Each party can provide guidance as to how it expects its MPs to vote on any particular question; there may be varying degrees of penalty if that guidance is ignored, but the worst that can happen is that the party disowns the MP: it cannot prevent the MP voting in Parliament according to how that MP chooses.