At its extreme, the "will of the people" can spill over into mob rule, in which case minorities need their rights safeguarded. Remember Hitler often operated by getting his actions approved by plebiscite.

The situation is complicated by the UK's not having a written constitution, so the judges will come to their decision using "precedence".

The way I see it, the following facts are material:

1) In the UK's system of representative democracy, referendums are not a normal way of governing.
2) When the UK entered the Common Market, the referendum result was enabled by Parliament, so the same should apply on leaving.
3) In the recent unsuccessful referendum on voting reform, the terms were specifically included that parliamentary approval would not be required. The fact that no such rider was enshrined in the Brexit referendum implies that parliamentary approval is necessary.
4)Triggering Article 50 without parliamentary approval is tantamount to governing by decree.
5)The fact that Scotland, Northern Ireland and Gibraltar all voted to remain in the EU raises serious constitutional issues.