Peter Bone MP has claimed fellow Conservatives want to see a change in Brexit negotiations and "not necessarily in the leader of the party".
Appearing on the breakfast show, Mr Bone said that "many, many Tory MPs are unhappy" with ongoing negotiations, but wouldn't want a change in leader at this stage.
"Many, many Tory MPs are unhappy about the Brexit negotiations and they want to see a change in the negotiations, not necessarily in the leader of the party, and that's the thing that people need to understand. It's a change in the direction of the Brexit negotiations, not changing the leader, that's important," he said.
His comments followed Theresa May's meeting with backbenchers on Wednesday, in which she delivered an "emotional and personal speech that won the room" according to former home secretary, Amber Rudd.
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Ahead of the meeting, an anonymous MP had told the press that Ms May should "bring her own noose", which sparked backlash from fellow politicians, and calls for whips to reveal the identity of the MP.
Mr Bone told Julia Hartley-Brewer there was a way to "unite most Conservatives" on Brexit by requesting a free trade deal similar to Canada's.
"If the Prime Minister went to Europe and said, 'Look, we want a free trade deal rather like you've done with Canada, and make it a little bit stronger' - because that's a benefit for both the EU and us - I reckon that would command an overwhelming majority on Conservative benches," he said.
"That's really what Conservative MPs like myself are trying to press the Prime Minister into doing. Hopefully she will get so fed up with the EU negotiators that she will go for that option. That would be the best solution but time is running out."