Re: This is why you write down your constitution
Yes the Supreme Court does answer questions about what the US Constitution and its amendments permit or deny, but a basic question like "can the president undo existing law legally passed by congress?" is not something that would ever be at issue. The Supreme Court considers cases regarding stuff that's not specifically covered in our constitution, like the legality of abortion, exactly what limitations can be put on gun ownership, etc.
I'm sorry, but the question of who has the power to unmake existing law is pretty basic, so if you need a court to determine the answer to that... Like I said, if the PM can remove the UK from the EU without Parliament having any say, then he can pretty much do anything by undoing any previous acts of Parliament. Arguably he could put the Queen back in charge and take both himself and Parliament out of equation setting UK history back 350 years or so.
For that matter, wasn't it an act of Parliament that stripped Charles II's royal power to arbitrarily suspend laws passed by Parliament? Did they really mean to remove that power from the King, and give it to the Prime Minister? Could the PM undo that, or undo the Reform Act of 1832? If you take the position that the PM can unilaterally pull the UK out of the EU, you pretty much have to concede he has similar power to that of the King after the Magna Carta was signed as he can undo any law he wishes.