So the Brexiters forgot Britain is a Parliamentary Democracy..

on to advance it (or even curtailing if it seems to be folly).

This will be a delicate operation with many different paths.

People think they voted a series of measures were enacted automatically... I don't think so.

Referendums, and "popular votes" clash with the tenets of parliamentary representative democracies. Parliamentary Sovereignty is sacrosanct. To assume that a referendum could be self-executing without parliamentary say was a risk Cameron never should have taken - he just assumed Remain would have edged the Brexit vote. Parliamentarians now find themselves in a really awkward position - depending on how folks in their constituencies voted.

People in London for example would not want their parliamentarian to approve any measures
that go in that direction.

Depending on how population is distributed, and what parties represent the various districts, it is possible
that Brexiters don't have the vote in parliement to get things through.

As you said in your other post - things are going to get complex ( and potentially very ugly - even uglier than they are now) Farage is already throwing hissy fits.