"One of the reasons people voted to Leave was because they felt they were not getting a fair suck of the sauce bottle, as they say".
One source quoted by the BBC said "people feel the leadership is out of touch and has lost the plot" but another said changing the leader "is a stupid idea now".
He said, however, he personally was no part of any leadership challenge, while another MP who attended said only five or six MPs openly discussed removing May. But it broke up without a decision on a plan of action.
European Commission head Jean-Claude Juncker on Wednesday also renewed a pledge of close trade and security ties with Britain post-Brexit, helping lift sentiment.
"That seems to me to be a particular economic risk in Chequers and makes it substantially worse than the status quo", he said.
He said: "We have managed to reduce the great British Brexit to two appalling options: either we must divide the Union, or the whole country must accept EU law forever".
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But he questioned whether Johnson could unify the party as leader and "solve Brexit". This is seen as critical by both sides, but talks have been deadlocked for months.
Mrs May's spokesman said Chequers was "the only serious, credible and negotiable plan". "Brexit must be put back to the electorate in the form of a people's vote".
Mr Freeman said the advantage of having a contest next summer was that the issue of whether Brexit would happen would be settled by then and the party would, instead "be debating where we take it". "We are not far from agreement".
Any deal with the European Union must be approved by the British parliament, which is due to go on Christmas holiday from December 20 to January 7.
Barnier refused to comment on the divisions in the governing British Conservative Party over Brexit.
Mr Baker, a former chairman of the influential pro-Brexit European Research Group of Conservatives, urged Mrs May to negotiate a free trade agreement instead of the Chequers plan.
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The trade union movement is preparing to throw its weight behind a public vote on the final Brexit deal because of fears the United Kingdom is going to "crash out" of the EU. "Though most are unhappy with Chequers".
The ERG is unveiling its own alternative plan for tackling the Irish border issue on Wednesday.
The likes of former foreign secretary Boris Johnson, Environment Secretary Michael Gove and Home Secretary Sajid Javid are expected to be among the runners and riders whenever the PM leaves Downing Street.
"Brexit is a negative negotiation, unfortunately".
Devolution could see Yorkshire become 'England's Catalonia'George Freeman, who was chairman of the Prime Minister's policy board until November past year, said he believed Mrs May should "seal the deal" before handing over decisions about the long-term relationship with the European Union to a successor.
Rockfall at Navagio Beach in Zakynthos injures tourists
O'Connell described the piece of rock that fell as being as big as a four-storey building, crashing down onto the beach . Coast guard officials told the Evening Standard that those hurt had not sustained any life-threatening injuries.