South Suffolk MP James Cartlidge has joined the calls for Prime Minister Theresa May to resign as soon as possible – to give her successor the chance to negotiate a new deal with the EU before the end of October.
And his Conservative colleague Dr Dan Poulter, MP for Central Suffolk and North Ipswich, is also looking ahead to the time beyond Mrs May's premiership.
Mr Cartlidge said the Prime Minister deserved to be praised for her single-minded determination to get a Brexit deal - but she had now reached the end of the road.
He said: "Talking to people here (Westminster) this week, it is clear that there is no way any deal she puts forward now will get the support of the House of Commons.
"We have to remember the hard work she has put in, but now is the time for her to stand down and allow someone else to take over and try to negotiate a deal."
Mr Cartlidge felt it was important to get a new Prime Minister in place before the start of the summer recess at the end of July so the new leader can spend August preparing a new deal to be negotiated with the EU in the run-up to the October 31 deadline for the UK to leave.
Dr Poulter agreed that it now looked inevitable that a new Prime Minister would have to be chosen soon to take over well before the October deadline.
He said: "As someone who voted Remain but recognised the need to respect the democratic vote, it's clear that whoever leads the party now has to come from the Leave side of the referendum campaign.
"I certainly don't want to see another referendum because it would just divide the country even more - but I would want to see a new Prime Minister committed to the One Nation Conservative tradition rather than some of the more extreme right-wing policies we hear of from some people."
Neither Mr Cartlidge nor Dr Poulter felt there was any chance of the Prime Minister's new deal getting through the Commons - and they both said there was no point in bringing it back to the House. They have both backed her deal at every vote.
Dr Poulter said: "She has had a very tough three years as Prime Minister - she's worked very hard on the deal. But as someone who voted Remain, she's been unable to get the support of some elements of the party and it's time for someone else to take over as leader."
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