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Prime Minister Theresa May is reported to have indicated that she intends to stand down once Brexit is through.
The PM is said to have told backbench MPs at a meeting of the 1922 committee that she is prepared to stand aside once the first phase of the UK's departure from the EU is complete.
The announcement is likely to help her secure enough support from MPs to back her deal and get it over the line.
It comes as MPs are discussing eight alternative options for Brexit after Parliament seized control of the Brexit process.
Another of the county’s MPs indicated today that he was prepared to back the deal if it's came back to Parliament having previously voted against it twice.
Conservative MP Rehman Chisti, who represents Gillingham, said he was doing it with a heavy heart but Parliament was strongly in favour of remaining in the EU and he feared that MPs were determined to block Brexit from being implemented.
Addressing the 1922 Committee this evening, Prime Minister Theresa May said: “This has been a testing time for our country and our party. We’re nearly there. We’re almost ready to start a new chapter and build that brighter future.
“But before we can do that, we have to finish the job in hand. As I say, I don’t tour the bars and engage in the gossip – but I do make time to speak to colleagues, and I have a great team in the Whips' Office.
“And I have heard very clearly the mood of the parliamentary party. I know there is a desire for a new approach – and new leadership – in the second phase of the Brexit negotiations – and I won’t stand in the way of that.
“I know some people are worried that if you vote for the Withdrawal Agreement, I will take that as a mandate to rush on into phase two without the debate we need to have. I won’t – I hear what you are saying.
“But we need to get the deal through and deliver Brexit. I am prepared to leave this job earlier than I intended in order to do what is right for our country and our party.
“I ask everyone in this room to back the deal so we can complete our historic duty – to deliver on the decision of the British people and leave the European Union with a smooth and orderly exit.”
Paul Cooper, the chairman of the Faversham and Mid Kent constituency Association, said: "It is time to move on from the Brexit debate and that clearly can only be done with a new leader."
Keep up-to-date with all the latest as MPs get ready to vote on our live blog.