Its already being debated whether Article 50 invocation requires an Act of Parliament or not. I cant judge the constitutional issue (can anyone?), but practically speaking it seems to me that if Parliament says it requires their explicit consent than it does. Similarly, if Parliament washes its hands of the matter, who or what can overrule them and make them vote if they dont want to? So I see a few scenarios in this multi-stage game:
1. Parliament wants no vote in the matter, and claims it doesnt have to vote. In this scenario, the new PM may not act on it either. Note that Theresa May was originally pro-Remain, she will believe that Article 50 will worsen the recession and thus her electoral prospects, and she wouldnt have parliamentary approval as cover for pushing the nuclear button. If I were in Parliament, with a moderately pro-Leave constituency, I would be rooting for this scenario. No one acts, but everyone can blame other parties for not acting.
2. Parliament cannot run away from its voting rights, or even positively seeks to assert them. Under this scenario, commentators may suggest that Parliament as a whole has to desire Brexit, if only to keep its legitimacy. But recall that before the referendum, Parliament as a whole was about 3-1 pro-Remain. Why chase after a voting right you dont wish to have? If Farage didnt want to stick around for such an outcome, why should you? So vote Remain, claim you had initially campaigned along with pro-Remain forces, claim you are sticking to your original electoral mandate, and see what happens to your political future. Say it is the others who are detaching Parliament from the will of the people.
3. The 2017 PM and Cabinet take to the British people an alternative, non-EU vision of what Leave would look like, but they dont lie too much to make it look so great. They hold a second referendum, not on Leave vs. Remain per se, but on whether that is a satisfactory target option for a Leave scenario. In fact they can design the plan to fail simply by being somewhat realistic. The option fails, and the politicians claim everyone has to go back to the drawing board. I get sick of my Twitter feed being full of so much Brexit talk for so many years, and I stop following so many British people.
4. The trickling, tortuous uncertainty through Fall 2017 is so economically costly that everyone realizes a decision must be made and soon. Leave is the only decision which is focal, because of the referendum, and so Leave is set in motion and Article 50 is invoked. You will note that this scenario, while it sounds plausible, is a bit at odds with waiting until Fall 2017 to begin with. So the reality of waiting today has to lower the probability of this one somewhat.
5. The trickling, tortuous uncertainty through Fall 2017 is so economically costly that everyone realizes a decision must be made and soon. Leave is a more focal decision, but it still takes years to negotiate and consummate, thereby ensuring the uncertainty continues to kill the British economy. Leave therefore is discarded through political shenanigans and Remain rules the day because only the status quo ex ante can be brought about so quickly.
6. In the meantime, the EU does something really stupid, which includes the steady insulting of the British people and government, and almost everyone in the UK wants to leave by Fall 2017.
6b. In the meantime, Putin does something really stupid, and English opinion shifts strongly to Remain and Remain comes about through emergency national security channels.
7. In the meantime, the French and German elections require those governments to reassert at least partial control over their borders vis-a-vis immigration. This right is then offered to the UK, if only verbally, and the support for Leave more or less collapses. There is the beginnings of negotiation for a new EU treaty, in the meantime a bunch of EU nations including the UK break the rules of the old treaty, yet without being punished. This strikes me as one of the more plausible scenarios.