The majority vote doesn't apply here though, precisely because the act that brought it into being said so, and because we have representitive democracy.
This wasn't an exercise in direct democracy, it might have been portrayed that way, but it wasn't.
A majority IS needed in a general election yes, but after that not. This was not a general election or a binding referendum so therefore the majority rule is not valid here.
As agreed by the courts and will be agreed by the court of appeal.
It needs to be passed through parliament, and in a representative democracy where the vote was so close, and as admitted the factions within the leave vote so diverse, it is imperative that it is debated.
Not ignored, debated and agreements made on further progress.
Going forward without parliamentary approval or debate on how to proceed would be the undemocratic thing.