As I understand things, the Bill requires the PM to ask the EU for an extension to Article 50, thus putting off leaving the EU for a period to be agreed with the EU.
Noises from Brussels are said to indicate that the EU is willing in principle to agree a deferral, because EU negotiators don’t want a ‘No Deal’ exit either.
Further, it is generally accepted that the PM is bound by our constitution to request the Queen’s assent to the new law, and if he refuses to do so, thereby breaking the law, he must resign.
If he resigns, the Queen will summon one of her parliamentarians, i.e. one commanding a majority, to form a new government and fulfil the requirements of the new law by seeking an extension.
BJ would return to the back benches to lick his wounds. During the extension, of whatever duration was agreed, decisions would have to be taken about if, when and how the nation’s withdrawal from the EU should eventually be effected.
There would likely be a general election to give public legitimacy to a new government, replacing the interim one produced by BJ’s resignation.
This newly elected government, having a fresh mandate from the electorate, would be empowered to provide a general framework for deciding definitively our relationship with the EU, and everything else needed to run the country effectively and, perhaps, more coherently and fairly in very challenging times worldwide.
That’s all dependent on the wheels not coming off the constitution altogether, and the country coming under dictatorial authority where one individual and his/her cronies decides without reference to public opinion what happens everywhere and always just because they say so. And dissent is arbitrarily and secretly crushed wherever it has the temerity to raise its subversive head.