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 said Mr Johnson should “consider his position” in a short statement to the party’s conference in Brighton.
The SNP’s Ian Blackford, speaking outside the High Court, said: “Boris Johnson must resign immediately.”
Downing Street has said it is “currently processing the verdict”.
Mr Johnson suspended – or prorogued – Parliament for five weeks earlier this month, but the court said it was wrong to stop MPs carrying out their duties in the run-up to Brexit on 31 October.
The PM has promised the UK will leave on that date, with or without a deal with the EU.
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.
Parliament will resume sitting at 1130 BST on Wednesday.
In a statement outside Parliament, Commons Speaker John Bercow said there would be no Prime Minister’s Questions, but there would be scope for urgent questions, ministerial statements and emergency debate applications.
Opposition MPs say they plan to use Wednesday’s session to hold Mr Johnson to account for his decision to suspend Parliament – and potentially begin moves to oust him has prime minister.
Liberal Democrat leader Jo Swinson said Mr Johnson’s actions had shown he was “not fit to be prime minister” and he should resign.
Mr Blackford said: “If he doesn’t go, Parliament will have to remove Boris Johnson.”
Labour MP Stephen Kinnock said opposition parties were likely to table a vote of no confidence in the prime minister once they could be sure a no-deal Brexit had been ruled out.
He said Mr Johnson was unlikely to stand down of his own free will and would “squat in Number 10,” adding that MPs would have to “take matters intro our own hands in Parliament”.
Jeremy Corbyn had been due to deliver his keynote speech at Labour’s conference on Wednesday but will now address delegates later on Tuesday.
Earlier, he told activists Mr Johnson would become “the shortest-serving prime minister there has ever been” if he resigned.
He added: “So, obey the law, take no-deal [Brexit] off the table and have an election to elect a government that respects democracy, that respects the rule of law and brings power back to the people – not usurps it in the way that Boris Johnson has done.”
At the end of Mr Corbyn’s short statement, Labour delegates chanted “Johnson out”.
There were emotional scenes outside the High 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 was “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.”
Brexit Party leader Nigel Farage described the prime minister’s decision to suspend Parliament as “the worst political decision ever” following the Supreme Court defeat.
He called for Mr Johnson’s chief adviser, Dominic Cummings, to quit.