BJ doesn't vote in Uxbridge because he doesn't live there.
Bear in mind that turnout is a percentage of those on the electoral roll, and plenty aren't, especially the young, the poor and the socially marginal.
MPs are elected to represent their constituents, all of them, not just the ones who voted for them, not just the ones who voted, not even the ones on the roll, but the entire population. It is for this reason that the Tory gerrymander in the guise of 'equal' constitiencies when the rates of voter registration are far from equal, is such a con job.