MPs are first and foremost representatives of their constituency (i.e. local area). Their job is to represent the desires and interests of those people.
The government should be working on Brexit, supported by MPs of areas who voted to leave.
MPs of areas that voted remain should be either working against Brexit, or working to have concessions made as part of the Brexit agreement to represent the wishes of their constituency.
As much as it may annoy you across the pond, the MPs representing their specific constituency is a feature not a bug.
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