Opposition leaders have demanded that Boris Johnson reverse his decision to suspend Parliament or put it to a Commons vote.
It came as Labour leader said that as soon the House of Commons returns on Tuesday his party would begin the process of voting to stop no-deal from happening.
Mr Corbyn said: “What we are going to do is try to politically stop him on Tuesday with a parliamentary process in order to legislate to prevent a no-deal Brexit and also to try and prevent him shutting down parliament in this utterly crucial period.”
“This country is in danger of crashing out on the 31st of October with no deal,” he said.
“We have got to stop that and that is exactly what we will be doing next Tuesday.”
In the joint statement the leaders of Labour, the SNP , the Lib Dems , Plaid Cymru, the Independent Group for Change and the Greens, said: “It is our view that there is a majority in the House of Commons that does not support this prorogation, and we demand that the prime minister reverses this decision immediately or allows MPs to vote on whether there should be one.
“We condemn the undemocratic actions of Boris Johnson following his suspension of parliament until 14 October.
“There is no mandate from the public for a damaging no-deal Brexit.
“The prime minister is shutting down parliament with the sole aim of stopping MPs from avoiding a no-deal Brexit.
“This will be the longest prorogation in recent history, and one that comes at a critical moment in the history of our respective nations and the Brexit process.
“Voters are being deprived of the opportunity to have their representatives hold the government to account, make any key decisions, and ensure there is a lawful basis for any action that is taken.”
Mr Johnson said the suspension was necessary so he could put forward his Government’s new legislative agenda, and in order to do this through a Queen’s Speech, the current two-year session of Parliament must formally come to an end.
Leader of the House of Commons Jacob Rees-Mogg hit back at the PM’s critics, saying the outpouring of outrage it triggered was “phoney”.
It comes as backbench Tory rebels have started working with opposition MPs to try to force the Prime Minister not to take the UK out of the EU without a deal.
Former justice secretary David Gauke said next week will be crucial for MPs hoping to block a no-deal Brexit.
Speaking to BBC News, Mr Gauke said: “We are very concerned about what no deal is going to involve.
“It’s probably not in our interests to be very specific about what the proposals might be as to how we would do that.
“I think there are many of us who would be inclined to say that Parliament doesn’t need to take action for a while yet.
“But given the announcement from (Wednesday) that Parliament is only going to be sitting for a week next week and then really at the end of October, by which point it will be too late for Parliament to do anything effective.
“Then I do think we have to look at what our options are next week.”
He added: “The fact is there isn’t a mandate for a no-deal Brexit. It is not what was campaigned for in 2016.
“It is not what the public want according to opinion polls, only about a third of the public would support that and I think as the consequences of no deal become clear, that number may well fall.
“So I think Parliament does have a responsibility to act and it may well be that next week is the only opportunity for us to do so.”