In an open letter, the opposition MPs branded the move an "unconstitutional coup" and said parliamentarians must not allow the government to "avoid scrutiny at this time of national crisis".
Thousands of demonstrators are expected to take to the streets across the country today as fury mounts over the prime minister's plan to prorogue parliament for more than a month ahead of 31 October.
Tory MPs Guto Bebb and Antoinette Sandbach have signed the letter alongside Liberal Democrats leader Jo Swinson, Independent MP Heidi Allen, Green MP Caroline Lucas and representatives from the SNP, Plaid Cymru and The Independent Group for Change.
The letter, coordinated by pro-Remain group Best for Britain and published in The Guardian, said: "In less than two months Britain could crash out of the European Union without a deal. Those who voted to leave in 2016 were promised a negotiated deal by the Vote Leave campaign.
"The prime minister has now announced that he will prorogue parliament in a bid to get a no-deal Brexit through.
"Such an unconstitutional coup risks compromising people’s jobs, security and living standards, not to mention the Good Friday Agreement. Now Boris Johnson is jeopardising all this for the sake of his own personal polling.
"It is clear that this has been done to stop MPs debating Brexit at our country’s most constitutionally charged time in recent history. We cannot allow the government to avoid scrutiny at this time of national crisis.
"We call for MPs to sit at an alternative parliament to continue holding the government to account and fight this most damaging Brexit."
The move comes after senior opposition party figures gathered at Church House - the wartime home of parliament - where they agreed that shutting down parliament would be a "democratic outrage".
Meanwhile, around 80 protests were due to be held across the UK on Saturday, as hundreds of thousands of demonstrators were expected to express their fury at Mr Johnson's prorogation plan.
Shadow chancellor John McDonnell, who will attend protests in London, urged other MPs to take to the streets in opposition.
"Whether you voted for Remain or Leave, the people did not vote for a No Deal for which there is no mandate," he said.
“As elected Labour MPs across the country represent their constituents by joining in these protests, I urge other MPs to think of their constituents whose jobs and livelihoods will be put at risk in a no-deal Brexit.
“If Boris Johnson wants a mandate, then he should call a general election and put it to the people.”
Momentum, the influential left-wing grassroots network, said it was expecting hundreds of thousands of people to turn out to protest.
Laura Parker, Momentum’s national coordinator, said: “We have a barely-elected millionaire prime minister who is happy to exploit a loophole in our flawed democracy to force through a Trump first, no deal Brexit.
"He is part of the same tiny, privileged elite which has been hoarding power at the top and eroding our democracy for decades.
There are thousands of people from all over the UK and across the political spectrum who will protest to stop Johnson close the doors on our democracy."
It comes ahead of an explosive week in Westminster, when rebels MPs will attempt to block a no-deal Brexit before the prime minister can shut down the Commons.
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