Tom Brake has accused politicians across Europe of "concentrating on their Christmas dinners" rather than Brexit.
Appearing on the Mike Graham show, the Liberal Democrat MP said it was "very clear" that little had been done to further negotiations over the festive period.
"What the Prime Minister did before Christmas was say 'Well I need some time to go away and negotiate, and then I'll come back with a fantastic new deal'," Mr Brake said.
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"What is very clear is that over Christmas and New Year, politicians around Europe have concentrated on their Christmas dinners. There has been no activity at all apart from, apparently, one phone call to the Spanish Prime Minister."
The politician revealed he supported a letter organised by Conservative MP Dame Caroline Spelman and Labour MP Jack Dromey, calling on the Prime Minister to rule out a no-deal Brexit as March 29 nears.
'Perfectly possible' to prevent no-deal Brexit
Theresa May leaves Downing Street. Image: Getty
"It would be perfectly possible for the government to make time available for a small piece of legislation that says no-deal is ruled out," Mr Brake said.
"If a majority of MPs in the House of Commons say to the Prime Minister we do not want no-deal, you have to rule it out. It would be rather unconstitutional for Ms May to turn round and say 'Well I'm disregarding the views of the majority of the House of Commons and I'm going to proceed with this any case'".
He added: "Even if half of what is predicted [in event of no-deal] doesn't happen, and the other half does, it has such an impact."