More than 200 MPs from various parties have signed a letter urging the government to take the prospect of a no-deal Brexit off the table.
The politicians are from the Conservative, Labour, Liberal Democrat, SNP and Plaid Cymru parties and the letter was written by Meriden MP Caroline Spelman and Birmingham Erdington MP Jack Dromey.
The group is concerned about the effect of a no-deal Brexit on the manufacturing industry.
They wrote: "The renaissance of manufacturing and its supply chains in this country, bolstered by demand for exports, has markedly improved the lives of our constituents.
"The principal market for these exports has been the European Union.
"The revival of the manufacturing industry has created innumerable jobs, not only via direct employment but also in the supply chain and ancillary services."
They added: "Leaving the EU without a deal would cause unnecessary economic damage.
"Trading on World Trade Organisation terms would instantly make our manufacturers less competitive and make it very difficult for the industry to justify producing goods in the UK for export.
"Leaving without a deal would make continued investment in UK manufacturing a real challenge for global firms, when they have plants in other European locations.
"Without continued investment and confidence in the UK manufacturing sector, thousands of jobs across the country will be put at immediate risk."
The letter has been backed by business organisations such as the Confederation of British Industry, manufacturers' organisation EEF, the Federation of Small Businesses and the Society of Motor Manufacturers and Traders.
The chief executives of Airbus, Jaguar Land Rover, Ford and Rolls Royce are also supporting it and will be meeting MPs in parliament on Wednesday evening, while the prime minister has invited the 209 MPs to meet her at Downing Street on Tuesday.
It comes hours after some Tory Brexiteers appeared to be willing to risk a no-deal exit from the EU.
One told Sky News that MPs' attitudes had recently "hardened" towards a belief leaving the EU without a withdrawal agreement would be "absolutely okay".
With the House of Commons due to vote on her EU exit agreement in the next 10 days, Theresa May has warned MPs the country will be in "uncharted territory" if they vote down her deal.
The parliamentary showdown is expected on 14 or 15 January, with the prime minister preparing to set out "assurances and measures" over the next few days as she tries to convince sceptical MPs.
These include specific measures relating to Northern Ireland, plans for a greater role for parliament in Brexit decision-making, and further assurances from the EU amid concerns about the so-called backstop arrangement for the Irish border.
On Sunday, Mrs May sidestepped questions about whether she could keep putting her deal back to MPs if it is rejected a first time round.
She also attacked those campaigning for a second EU referendum for "disrespecting" Leave voters, while she accused Labour – who will vote against her deal – of "playing politics" in order to create the "greatest chaos".
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In a message also issued to her own party's Brexiteer MPs, Mrs May said: "We have got people who are promoting a second referendum in order to stop Brexit, and we have got people who want to see their perfect Brexit.
"I would say don't let the search for the perfect become the enemy of the good because the danger there is that we end up with no Brexit at all."