The "constitution" in the UK is so incredibly complicated, ever changing, and confusing with layers of hierarchy and sub-hierarchy within elements. What's in at one moment and out the next. I guess it is the epitome of common law over enumeration, but it is very problematic and chaotic coming from a US legal mindset.
As a matter of law, it should come down simply to what does it take in UK constitutional law to exit a treaty. Can a PM unilaterally exit some other treaty without parliamentary approval? With or without cabinet approval?
If it is a matter of rights given cannot be taken away without parliament assent, then I'd say rights created in treaty are not created in law unless parliament passes a law codifying those rights. If they do, then exiting the treaty is irrelevant because the UK law still exists, which I understand to be the fact in this case.
Then there is the lesser question if parliament's authorization of the referendum implied a legislative intent to act on its result. That's a coin flip. The US supreme court would likely kick that back to congress calling it a political question, but the UK supreme court I've found to be far far far more political - I think owing to their origin in the house of lords.
I'm not nearly expert enough in British law, especially constitutional law, to give any kind of serious commentary on this case, but I'll be interested to read their opinion when they're done.