This is why you write down your constitution
Instead of relying on oral history or tradition or whatever the heck it is you lot are relying upon here. I will say you won't have moved much past having a King if the PM is able to undo by himself an Act voted upon by the whole of Parliament over 40 years ago.
It is one thing for the man in charge to have veto power, as the president in the US does. But his veto power only extends to something passed by congress that is not yet law. If he signs it, it is law, if he vetoes it, it is not law. The congress can override him with 2/3 vote in both house & senate but in today's partisan political world that's almost impossible to imagine. The president most certainly cannot veto something retroactively, which is basically what your PM would be doing if he is determined to have the power to unilaterally serve Article 50 notice to the EU and this is judged to have met the EU's conditions for constitutionality.
What would the PM who unilaterally removed the UK from the EU do for an encore, repeal the Indian Independence Act of 1947 so the UK legally considers India its colony once again?