British Labour leader Jeremy Corbyn has called for Mr Johnson to "consider his position" following the ruling.
He was speaking after the Supreme Court ruled that the decision to suspend parliament for five weeks was unlawful.
Addressing the Labour Party conference in Brighton, Mr Corbyn said: "It shows that the prime minister has acted wrongly in shutting down parliament.
"It demonstrates contempt for democracy and an abuse of power by him. The Supreme Court, therefore, passes the baton to the speaker to recall parliament.
"I will be in touch immediately to demand that parliament is recalled so that we can question that prime minister, demand that he obeys the law that has been passed by parliament and recognise that our parliament is elected by our people to hold our government to account.
"A Labour Government wants to be held to account. We wouldn't bypass democracy. And I invite Boris Johnson in the historic words to consider his position."
SNP MP Joanna Cherry, who led the case in the Scottish courts, said Mr Johnson's position was "untenable" and called on him to resign.
"This is an absolutely momentous decision. There is nothing to stop us - Members of Parliament - resuming immediately the important job of scrutinising this minority Tory government as we hurtle towards Brexit," she told reporters outside the Supreme Court.
"This is a huge victory for the rule of law and for democracy. As regards Mr Boris Johnson, the highest court in the United Kingdom has unanimously found that his advice given to Her Majesty the Queen was unlawful.
"His position is untenable and he should have the guts for once to do the decent thing and resign."
Mr Corbyn has moved his conference speech to this afternoon so he can attend the resumption of parliament tomorrow.
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Elsewhere, Liberal Democrat leader Jo Swinson said the decision by the Supreme Court confirms that Mr Johnson "isn't fit to be prime minister".
"He's misled Queen and country, and unlawfully silenced the people's representatives," she tweeted.
"I'm on my way to resume my duties in the Commons and stop Brexit altogether."
Independent MP and former attorney general Dominic Grieve said he was "not surprised".
The former Conservative MP said: "I am not surprised with the judgment due to the gross misconduct by the prime minister."
"It was perfectly obvious that the reasoning and motivation for suspending parliament was bogus and untrue and the reasons given, and I am delighted that the Supreme Court has stopped this unconstitutional act in its tracks," he added.
"What he should now be doing, the Prime Minister, is pausing and reflecting the untold damage he's doing to our institutions by his reckless and relentless desire to achieve Brexit on October 31, and actually start engaging with the dialogue in the House of Commons, and how we get out of the hole we have succeeded in digging ourselves into as a country."
The calling of a Queen's Speech and prorogation is the worst political decision ever. Dominic Cummings must go.— Nigel Farage (@Nigel_Farage) September 24, 2019
The European Parliament's Brexit co-ordinator Guy Verhofstadt tweeted: "At least one big relief in the Brexit saga: the rule of law in the UK is alive & kicking.
"Parliaments should never be silenced in a real democracy.
"I never want to hear Boris Johnson or any other Brexiteer say again that the European Union is undemocratic."
DUP leader Arlene Foster said the judgment of the Supreme Court had to be respected.
Ms Foster said her party "always respected the principle of the separation of powers upon which our constitutional law is founded".
"Therefore the judgement of the Supreme Court has to be respected," she said.
The Taoiseach has said the decision of the Supreme Court in London was "very much an internal matter" for the UK.
Speaking in New York, Leo Varadkar said he did not think it would be helpful for the Irish Government to comment on it.
He said as things currently stand, his meeting with Mr Johnson was due to go ahead later today at the UN.
However, Mr Varadkar said he "appreciates that may need to change".
Sinn Féin leader Mary Lou McDonald has said the judgment shows that Britain is experiencing a constitutional earthquake.
Speaking before the Dáil meets this afternoon, Ms McDonald said Mr Johnson must understand that the Irish question is not going away.
Ms McDonald added that Ireland cannot be the collateral damage for the Mr Johnson's ambitions and she called all sides in Leinster House to stand firmly behind the backstop.