Francis Hoar, a barrister specialising in public law, writes in The Independent that the government’s authority to trigger Brexit flows from parliament and is in accordance with constitutional principles:
The referendum it concerned was authorised by an Act of Parliament introduced by a government elected on a manifesto commitment to follow its result; it was enacted on the express understanding that the government (not Parliament) would withdraw in the event of a Leave vote; and the prime minister, during the campaign, undertook to give notice under Article 50 in that event. Save for one reference to the legal effect of a referendum being advisory in a House of Commons paper, the intention of Parliament was to delegate the decision to the electorate.
And what of the political effect? Parliament has already enacted a referendum on the understanding that it would respect the will of the people. The only decision that the people have made is to leave the EU and the only way in which it can be put into effect is through notification by Article 50. So Parliament has had its sovereignty “restored” in order to choose between respecting the result of a referendum it legislated for or to ignore it. It may do no more.