The chair of the European Scrutiny Committee has claimed Theresa May is "clutching at straws and clinging to wreckage" with her Brexit deal.
Sir Bill Cash made the comments on the breakfast show, and added that he thought the Prime Minister could not "continue in office" after losing the support of many Conservative MPs.
"There's a general sense that it's just clutching at straws and clinging to wreckage," he told Julia Hartley-Brewer.
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"There are people - and I'm certainly one of them - who can't accept this withdrawal agreement. It just doesn't make sense in the national interest, which is what they keep on asserting."
The Conservative MP for Stone said he had written a letter to the 1922 Committee "some weeks ago" over "badly conducted" Brexit negotiations.
"It is time people began to think hard about the fact that you cannot continue in office if the result of that is that you are effectively losing credibility in the House of Commons on that scale," he added.
"You can't go on clinging to the wreckage."