I think the importance that Worth assigns to the vote on Queen's speech is overrated in the present circumstances. And I'm not the only one to think so:
Usually, if the government lost such a vote, it would be expected to call an election, but to do this UK Prime Minister Boris Johnson would need support from two-thirds of MPs — which he doesn't currently appear to have.
"We could end up in a very strange scenario where the government can't pass its Queen's Speech but still can't get the numbers for a general election, said Thimont-Jack. "This has never really happened before and it's unclear what will happen next.
If he loses the vote on Queen's speech Johnson will probably lambast the MPs again calling them chicken for not agreeing to an election etc. They'll call again on him to resign, which he probably won't do. Actually he seems to have said that on Oct 14:
Boris Johnson will not resign if British MPs hand him another defeat by voting down his legislative agenda set out in the Queen’s Speech, Downing Street has said.
Number 10 also made it clear the British Prime Minister could plough on to introduce all the Bills announced, even if the British Parliament rejected his Government’s programme.
Opposition leaders accused the PM of using the speech as a pre-election stunt to win over voters, while Jeremy Corbyn branded it a “farce”.
Asked if Mr Johnson would resign if he is handed such a blow, the Prime Minister’s official spokesman flatly replied: “No.”
He later added: “If MPs do choose to vote against the Queen’s Speech it will be up to them to explain to the public why they are voting against greater support for our public services, including police, schools and hospitals.” [...]
And asked whether the PM could continue to progress the bills through Parliament even if the speech is defeated, his spokesman replied: “Yes, you can.”
Brexit legislation will probably still get discussed, because otherwise anti-no-deal-Brexiteers would have to gamble that the EU will offer an extension and that Johnson will not pull another stunt on it, like not signing something.
The EU is not looking forward to decide on the extension request. They want to see first how a vote on the deal goes in Westminster:
EU ambassadors agreed on Sunday morning that the withdrawal agreement would be sent to the European parliament on Monday. MEPs could vote on it on Thursday if the Commons has given its approval by then. [...]
The European council’s president, Donald Tusk, will spend until Tuesday consulting the heads of state and government about their appetite for a further Brexit delay. Ambassadors for the EU27 did not discuss the issue on Sunday morning.
Nevertheless, if that Westminster deal vote is not forthcoming, they'll probably approve an extension
Senior EU officials said it had been clear during the discussions among the leaders at a summit on Thursday that they would grant an extension. “Even [the French president Emmanuel] Macron in the room didn’t suggest otherwise”, a source said.
We'll have to wait and see if there's a majority in Westminster for not holding that deal vote (again). It seems doubtful to me that there won't be a deal-legislation vote given the position of Letwin etc., who actually support a deal.