I'm going to give the opposite answer to o.m.: the UK's traditional constitutional arrangement is that the executive has the negotiating power. Therefore the Government - and I think in fact the PM acting alone - could withdraw Article 50. The PM would probably then be forced to resign, although that's long overdue anyway given the number of spectacular vote defeats.
What's more of a problem is the Withdrawal Act and its effect on UK law (it has, and cannot have, any effect on the EU). It's rather hard to parse but my reading of that is that the commencement of section 1, Exit Day, depends on the action of a Minister. This may or may not already have happened.
(Other sections have already passed large amounts of lawmaking power to Ministers, which in the event of us actually leaving the EU effectively transfers authority from everything that was EU-governed directly to the PM. Not Parliament.)
Of great importance is the Wightman case. That was litigated on the opposite question: can Parliament unilaterally revoke Article 50? Consider para 105:
if, as a result of action carried out in accordance with its constitutional requirements (for example, a referendum, a meaningful vote in Parliament, the holding of general elections which produce an opposing majority, among other cases), the Member State’s initial decision is reversed and the judicial and constitutional basis on which it was sustained subsequently disappears, I also believe that it is logical, in line with Article 50(1) TEU, that that State can and must notify that change to the European Council.
This makes it quite clear that the state is separate from Parliament. Parliament can oblige the state to revoke article 50, but that's not the only route to valid revocation.
Also consider Miller: the government's case was that it could issue Article 50 without Parliamentary approval, but this was denied on the basis that doing so caused a change in UK domestic law and therefore required approval. Un-issuing article 50 should return us to the status quo, not changing UK law, and could therefore be done unilaterally by the government.