The MPs – including both Leave and Remain supporters – have been invited to meet the prime minister on Tuesday.
Tory ex-cabinet minister Dame Caroline Spelman, who organised the letter with Labour MP Jack Dromey, said a no-deal Brexit would cause job losses.
It comes ahead of a crucial Parliament vote on whether to back Mrs May’s deal.
The PM’s deal – which covers the terms of the UK’s divorce and the framework of future relations with the EU – has already been agreed with EU leaders.
But it needs to pass a vote by MPs before it is accepted. The vote is expected to happen on either 14 or 15 January.
The UK is due to leave the EU on 29 March 2019 whether the deal is passed by MPs or not.
Meanwhile, writing in Daily Telegraph, former Foreign Secretary Boris Johnson said the option of leaving the EU with no deal is “closest to what people actually voted for” in the 2016 EU referendum.
And Tory MP Damian Green – also an ex-cabinet minister – said the onus was on the MPs to say what deal they would support.
It comes as a major exercise involving more than 100 lorries is being carried out in Kent to test out how to manage traffic queues near the Channel ports in the event of a no-deal Brexit.
‘United on one thing’
Dame Caroline Spelman – a Remain supporter who was environment secretary for two years when David Cameron was prime minister – told BBC Radio 4’s Westminster Hour programme that 209 MPs had signed the letter.
She said: “Crashing out of the EU without a deal will cause job losses and bring to an end the renaissance of manufacturing that we’ve seen in regions like mine in the West Midlands, and both Jack Dromey and I know the human interest and impact of this.”
Asked if the prime minister “gets it”, Dame Caroline said: “Yes, I definitely think she gets it. She wouldn’t have invited us to come in and see her if she didn’t.”
Dame Caroline said the signatories to her letter included Brexit and Remain supporters – but the letter did not bind them to supporting the PM’s withdrawal deal.
Instead, Dame Caroline said, it creates a “platform”, which would “stabilise the economy and give reassurance to manufacturing”.
“We are united on one thing – we want to protect jobs and livelihoods by making sure we don’t crash out without a deal,” she said.
“If Parliament gives expression to not wanting to crash out without a deal, it means effort has got to be renewed to find an agreement which is acceptable to a majority of parliamentarians.
“Taking a step back and at least agreeing we’re not going to crash out without a deal means that on 29 March we’re not just going to fall over the cliff edge.”
Boris: ‘No deal is popular’
Mrs May’s deal is facing opposition from many of her own MPs, as well as Labour and other opposition parties including the Remain-supporting Liberal Democrats.
The DUP – which Mrs May’s Conservative Party relies on for a majority in Parliament – has said it will not back the deal.
Many Conservative MPs continue to believe the deal does not represent the Brexit the country voted for, and some are actively calling for Britain to leave with no deal.
If the UK leaves the EU without a deal, it would automatically fall back on World Trade Organisation rules – which would apply automatically to trade between the UK and EU.
- Reality Check: What does a ‘WTO Brexit’ mean?
- Could Channel Ports cope with no deal?
Writing in the Telegraph on Monday, Brexiteer Mr Johnson said of all the options suggested, the no-deal option is “gaining in popularity” and dismissed the warnings against it which he said were “downright apocalyptic”.
“In spite of – or perhaps because of – everything they have been told, it is this future that is by some margin preferred by the British public,” he said.
Mr Johnson said: “We must hope that Theresa May really does remove the backstop from the withdrawal agreement, in such a way as to give real legal protection to the UK.
“Failing that, we should approach the challenge of leaving on WTO terms in a way that is realistic and sensible, but also with the optimism and self-confidence displayed by the majority of the British public.”
On Sunday, Tory MP Peter Bone told Sky News the best way to “get on” with Brexit was to leave without a deal – which would be “absolutely OK”.
He said support for leaving without a deal was “hardening”.
But speaking on Sunday, Mrs May warned that if Parliament rejects her Brexit deal, the country faces “unchartered territory”.
The UK’s exit in March was “in danger” if MPs did not vote for it, she added.
As well as the invite to all signatories of the letter to Downing Street, Mrs May has also invited all Tory MPs to drinks receptions on Monday and Wednesday.