Chris

There is no legal means in the UK for Parliament to make itself subordinate to anyone or anything. As an institution, it is sovereign, which means the only thing it cannot do is pass any law that prevents it exercising its own will or that of a successor (each parliament lasting no more than five years, and being succeeded by another one after a general election).

The nearest parliament could have got to making the outcome of the referendum legally binding would have been to word the referendum act so as to explicitly mandate, via primary legislation, what the government was to do in the event of a leave or a remain vote. In that case, parliament would have had no role to play unless it chose to repeal that legislation.

The referendum act as passed did not have that effect, and so quite regardless of what the government may have intended, or what it printed on its leaflets, or how many MPs voted for it, the referendum is not binding. It is not possible for it to be so under our constitutional settlement. It took a civil war to establish that and it would take another one to undo it.

The argument in court was over whether the government was impinging on that parliamentary sovereignty by invoking Article 50 without parliament's consent. Parliament's consent is needed, the court ruled, because invoking Article 50 will inevitably lead to a piece of primary legislation being undone (the European Communities Act 1972). The government is not allowed to undo acts of Parliament. Only Parliament can do that (quite right too).

The only room the government has to argue their appeal is either to try to persuade the Supreme Court that Article 50 sets in motion a process that will stop a fraction short of annulling ECA 1972, or that us being ejected from the EU at the end of 2 years somehow doesn't have any ramifications for the ECA 1972 still being in force.

It's hard to see how they're going to pull that off.