I don’t claim to understand the historic place of referenda in the UK form of government. Brexit was the first I heard of it.
In any event, it appears to be what Americans would regard as “the law of the land.” Unfortunately, there wasn’t a due date for exiting the European Union.
The Government of the United Kingdom has also to date held eleven major referendums within the constituent countries of England, Scotland, Wales and Northern Ireland on issues of devolution, sovereignty and independence; the first such referendum was the 1973 Northern Ireland border poll and, as of 2018, the most recent is the 2014 Scottish independence referendum.
Plus three National ones - two on the Europe and one on Alternative Voting.
Referenda were considered against the British political system and only used by fascist states.
This referendum was only the third in British history and was shambolically arranged, with it being purely advisory and non binding as well as not putting a cut off on the total % of the electorate who should vote one way or the other (37% of the total electorate voted leave)
It was not the law of the land. What triggered the call for article 50 was parliament voting to do so in October 2016.
Remember, in the UK PARLIAMENT is sovereign NOT the people.
And there was and IS a due date to leave the EU. It was initially 29 March 2019 but the UK has twice begged to delay it