Jeremy Corbyn is leading calls for Boris Johnson to resign after the Supreme Court ruled the PM's decision to suspend Parliament was unlawful.
The Labour leader told his party's conference in Brighton the prime minister "has been found to have misled the country" and should step down.
The SNP and some Labour MPs said Mr Johnson could be ousted via a no-confidence vote, if he refused to go.
MPs will return to work on Wednesday at 11:30 BST after the court's ruling.
BBC political editor Laura Kuenssberg said one member of the government had joined calls for Mr Johnson to resign in the wake of the judgement, but, right now, that view was not widespread in the Conservative Party.
Mr Johnson suspended - or prorogued - Parliament for five weeks earlier this month, arguing it was necessary in order to hold a Queen's Speech and set out a new legislative programme.
But the court ruled it was wrong to stop MPs carrying out their duties in the run-up to Brexit on 31 October.
Supreme Court president Lady Hale said "the effect [of prorogation] on the fundamentals of democracy was extreme" and the government had provided no justification for it.
The PM has promised the UK will leave on 31 October, with or without a deal with the EU, but before the prorogation, Parliament passed a law intended to force a delay instead of allowing a no-deal exit.
It states that Mr Johnson has until 19 October to either pass a deal or get MPs to approve no deal - and if he fails, he must ask for an extension to the UK's departure date.
In a statement outside Parliament, Commons Speaker John Bercow said there would be no Prime Minister's Questions on Wednesday, but there would be scope for urgent questions, ministerial statements and emergency debate applications.
Opposition MPs say they plan to use the session to hold Mr Johnson to account for his actions - and potentially begin moves to oust him as prime minister.
Parliament twice rejected the prime minister's call for a general election earlier this month - under the Fixed-term Parliaments Act, Mr Johnson needs the support of two-thirds of MPs to hold a snap poll.
While opposition MPs said at the time they did want an election, they insisted they must first be sure that no deal could not happen.
Mr Johnson has said he will not ask the EU for an extension under any circumstances.
Now, however, the SNP's Westminster leader Ian Blackford has suggested the PM's opponents could not afford to wait.
"The opposition has to do its job - we need to remove him and we need do that through a motion of no confidence, leading to a general election," he said.
He continued: "It has to come quickly, we have to seize the moment, we cannot leave him in office, he has to be removed."
But Mr Corbyn, in his keynote speech at Labour's conference, said an election needed to take place "as soon as this government's threat of a disastrous no-deal is taken off the table".
The BBC's political correspondent, Iain Watson, said the Labour leader had made clear he would not call a vote of no confidence to trigger one until after the PM had sought a Brexit extension.
Shadow chancellor John McDonnell said the first step was to question Mr Johnson "about his behaviour" in Parliament and about whether he would comply with the law ruling out no deal.
"We will see what answers we receive from him and consider with other opposition parties what the next steps are," he said.
But he stressed: "I think the onus is upon the shoulders of members of the Conservative Party to make their decision about this man."
What could happen when MPs return?
Boris Johnson resigns - Highly unlikely given his defiant reaction to the Supreme Court verdict
No-confidence vote - If a majority of MPs back it and no alternative prime minister who can command a majority emerges within 14 days then there will be a general election
Censure motion - A non-binding slap on the wrist for the prime minister allowing MPs to register their disapproval of his actions without triggering his removal or an election
Impeachment - Being talked about by some Labour MPs but highly unlikely. No British prime minister has ever been impeached - only ministers - and the last attempted impeachment of a minister was in 1806
Liberal Democrat leader Jo Swinson said Mr Johnson had shown he was "not fit to be prime minister" and should resign.
Former Justice Secretary David Gauke was among the MPs expelled from the Conservative Party by Mr Johnson for voting against his Brexit plans, but he said he would not be calling for the PM to resign or backing a no-confidence vote in him.
"I think the prime minister can survive," he told BBC News, but only if he apologised for "what was done earlier this month in terms of proroguing Parliament" and changes his Brexit strategy and sacks chief adviser Dominic Cummings.
But the prime minister did receive backing from US President Donald Trump, who said Mr Johnson was "not going anywhere".
There were emotional scenes outside the Supreme Court in London as opposition MPs and campaigners hailed the court's unanimous verdict.
The SNP's Joanna Cherry, who pursued the case through the Scottish courts, said it was an "absolutely momentous decision" that made Mr Johnson's position as prime minister "untenable".
Green Party MP Caroline Lucas said: "Johnson must go and we must get back to work."
Businesswoman and campaigner Gina Miller, who challenged Mr Johnson's prorogation in the High Court, said the prime minister was not above the law.
She added: "MPs must get back and be brave and bold in holding this unscrupulous government to account."
Conservative former Prime Minister Sir John Major, who took part in the Supreme Court case, said; "No prime minister must ever treat the monarch or Parliament in this way again."
Brexit Party leader Nigel Farage said Mr Johnson must, "as a matter of honour", offer his resignation to MPs in Parliament on Wednesday.
He said he believed the prime minister and his advisers were "in trouble" and there must be a general election "before very long because Parliament and the government has ceased to function".