Conservative MP Peter Bone has told Julia Hartley-Brewer that if Theresa May's Chequers deal falls through, there is no alternative in place.
Appearing on the breakfast show, the Brexit Select Committee member said there was a "strong possibility" of a no-deal Brexit and "industry in particular" should be warned.
He said: "If we cannot strike a deal with the EU we have to tell industry in particular that we'll be coming out at the end of March 2019 on what people call a no-deal scenario.
"It is rather important that we tell people. There must be a deadline when we say we absolutely have tried to do a deal with the European Union but we can't do it, so we are actually going to come out without a formal deal."
"If she can't achieve Brexit she can't remain as Tory leader, surely?" asked Julia Hartley-Brewer.
'I don't think Chequers will be put to the vote'
Peter Bone says industry should be warned if no deal is reached
"If the most important plank of your government was put to Parliament and it was defeated, and it would only be defeated of course if Conservative MPs voted against it, then the normal situation would either be a general election or a new prime minister.
- Read more: ‘Scallop wars’: What will happen to UK fishing after Brexit?
- Read more: Former Brexit minister warns Tory party faces ‘catastrophic split’ over May’s Brexit proposals
"That's another very good reason I don't think Chequers will be put to the vote," Bone replied.
The Chequers deal has already been criticised by a number of MPs, including former Brexit minister Steve Baker and Boris Johnson, who received backlash after writing that the Brexit strategy was like a "suicide vest" around the British constitution in a column for the Daily Mail.
If the UK left the EU without a deal in place, it would fall back on its membership of the World Trade Organization (WTO).
UK exports to the EU would go through the same customs checks and taxes that are currently in place with countries such as the United States.