That's why we'd need an election, with one of the major parties standing as clearly pro Brexit, to draw a line under it. While I fully expect us to leave, and wish we would get a move on with it so we can get on with the rest of our lives, the Government, which was pro Remain until June 24, has no mandate to define the nature of Brexit, and it seems pretty confused about what it wants. An election is much safer than a second referendum for Brexiters, only takes a 2% swing for the result to change, less if more people get out to vote. And it's got to happen some time, let's get it over with.
Do you not see the irony of Parliament wishing to exercise its sovereignty on a matter of critical national importance, one of the things Brexit was about for the more principled end of the Brexit voter spectrum, and then being denied the chance? Although I don't think a majority of Brexit voters in Hartlepool give a toss about stuff like that, from what I saw of 3 minutes of QT.
Don't agree that the government has no mandate. In the referendum, the majority of voters voted to leave the EU. That's a mandate for a hard Brexit, since the referendum ballot paper was unqualified.
If there are compromises, as there no doubt will be after negotiations with the EU, then Parliament should be consulted.
The irony you point out can be turned on its head. Europhiles that were relaxed about handing increasing powers to Brussels now find they value Parliamentary sovereignty.