Gina Miller, an "investment manager," has brought a lawsuit challenging the constitutionality of the Brexit referendum, arguing that UK law requires a Parliamentary vote on the matter before the government can act on it.
The confusion over the issue is characteristic of the weird nature of the UK constitution. When I was studying to become a British citizen (note: despite what you may have heard, Britons are citizens, not subjects), I had to read the Life in the UK book and pass a test on it. One of the weirdest parts of it was the attempt to describe the UK's "unwritten constitution," a mishmash of court rulings, documents like the Magna Carta, European directives, and things that are just widely understood to be true.
Miller's argument is about the "ancient powers of Royal Prerogative." These are the powers reserved to the monarch -- who is represented by the executive, including the Prime Minister which can be exercised without Parliament's approval. Miller says that Royal Prerogative doesn't cover Brexit (which is obviously not something mentioned explicitly in any description of "ancient powers"), the government says it does.
BBC legal correspondent Clive Coleman suggests that this is a live issue, which could go either way.
The case has huge constitutional importance and should provide clarity on whether executive powers can, in effect, trump an act of Parliament.
Those bringing the case argue that legislation can only be altered by legislation. The government says it intends to give effect to the outcome of the referendum by bringing about the exit of the UK from the EU.
And that that is a proper constitutional and lawful step to take, using prerogative powers, in light of the referendum result and the democratic mandate it has provided.