The UK has no formal written constitution, though certain statutes, like the various Acts of Union that created it in the first place, certainly have the force of constitutional documents. But even absent a formal constitution, the principle of the supremacy of Parliament is clear. There are many things a government cannot do without the consent of Parliament, and I'm sure that entering into or abandoning international agreements are among them. Normally with a parliamentary majority it would be pretty much automatic, but I don't think that would happen in this case. Parliament cannot be bound by a referendum, it would view the result as just an advisory opinion and it's free to reject the advice.
And if it does, just watch the pro-Brexit folks shriek in righteous indignation because they don't understand how their parliamentary system works.
Maybe that's what the writer of the article I read meant. It was early this am so not sure.
Agree with you otherwise and honestly waiting to hear Blackie's view on it.