HM Gov't could take the decision unilaterally, but this particular HM Gov't doesn't have the kind of rock-solid majority in the Commons that would guarantee easy backing for the decision.

So we fall back on the hallowed convention that the House of Commons is sovereign. Ie, withdrawal of withdrawal would require a Commons vote.

A second referendum could satisfy the "democratic process" requirement, but would also require a Commons vote (as per the first referendum, established by Act of Parliament).

I used to be afew. I'm still not many.