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Ashford MP Damian Green has admitted a vote on the government's Brexit deal is unlikely to go through.
The government is to present MPs with its latest proposal in the coming weeks.
If it is defeated, Prime Minister Theresa May is expected to resign soon after.
Mr Green, a long-standing ally of Mrs May, says there is still a possibility a compromise could be brokered that would win support of MPs but that defeat is more likely.
Speaking on the latest edition of Paul On Politics on KMTV, he said: “I know that the strong expectation is that the vote won't go through - it hasn't gone through three times and why should the second reading of the bill be any different from the meaningful votes we have had before but let's see what happens.”
“There are a lot of Labour MPs who are spooked by Nigel Farage as there are Conservative MPs.
"In politics anything is possible but if you have to make a prediction and put your mortgage on it, you would say that the vote won't go through.
"At that point we will start the selection of a new leader.”
'In politics anything is possible but if you have to make a prediction and put your mortgage on it, you would say that the vote won't go through...' - Damian Green
He said that time being taken to arrange the UK's terms of departure “had led to the whole of the political system creaking".
“What has been injected into the political system is bitterness and hatred," he said.
Meanwhile, the Tonbridge and Malling MP Tom Tugendhat has said that the Prime Minister should resign straight away.
He said: “The time has now come for a change of leader and what we are now doing is running down the clock. What we really need to do is to get someone in place who can use the few months that we have until the end of October to come together and get a deal we can rally around.”
Mrs May is already under pressure to stand aside sooner rather than later from local Conservative constituency associations.
A meeting at which those associations are planning to discuss a vote of no confidence in Mrs May is scheduled for June.
Local party chiefs from three Kent associations are among those who have petitioned for a vote of no confidence - Gravesham, Faversham and Mid Kent and Maidstone.