Dominic Grieve has branded the impending confidence vote in Theresa May "crazy".
Appearing on the breakfast show, the former Attorney General claimed a leadership contest would serve "no useful purpose whatsoever", particulary at a time of "major national political crisis".
"Changing Prime Minister at the present time - particulary with the six week gap that would be required to do it - appears to me to be completely crazy," he told Julia Hartley-Brewer.
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"Efforts might be made to speed it up but ultimately the decision goes to the membership of the Conservative Party, which takes quite a lot of time to organise."
The MP for Beaconsfield, who has previously come out against the Brexit deal, added that the problem was not with Theresa May, but "the question that Brexit has posed".
"The truth of the matter is that this problem comes from Brexit, not the individual Prime Minister," Mr Grieve said.
'Destructive and not constructive'
He added that if someone who "believes passionately" in Brexit took over from Ms May, it could result in "chaos".
"Some of my colleagues who are in the ERG have, I'm afraid, an entirely mistaken view of what they can deliver in terms of Brexit," he said.
"As long as they have that, their role is going to be largely destructive and not constructive."