An internal Government document has revealed details on how ministers could be given a free vote on whether to expand Heathrow Airport.
The paper, which was filmed by a passenger on the LondonUnderground, discusses the "potential waiving of collective responsibility" ahead of the forthcoming decision on airport capacity.
The long-awaited decision on whether to expand Heathrow or Gatwick is politically highly sensitive for Theresa May due to divisions within the Tory ranks.
Foreign Secretary Boris Johnson campaigned against Heathrow expansion while London mayor, and Putney MP and Education Secretary Justine Greening is also opposed.
Details of the proposal were contained in an email sent to Sue Gray, the director general of the Cabinet Office's propriety and ethics team, Channel 4 News reported.
A Tube commuter spotted the email printout while standing close to the official on a Central Line train.
The passenger captured some of the contents with a smartphone, including a section clearly marked "waiving collective responsibility" and appearing to indicate that one option would be a free vote.
The disclosure is the second embarrassing document leak to hit the Government within days after the Prime Minister's plans for new grammar schools were inadvertently revealed to press photographers in Downing Street.
The email from Sharon Carter to Ms Gray states that lawyers and colleagues in the Cabinet Office's economic and domestic affairs secretariat "are seeking specific input from us on how to handle potential waiving of collective responsibility".
The document suggests that "one route for waiving collective responsibility would be a free..." with the next few words then obscured by the thumb of the woman holding the printout.
The sentence continues"... allowing ministers to speak against the Government's position in the House".
The document goes on to refer to the situation during the coalition government, when the Liberal Democrats and Conservatives held differing positions, and in the run-up to the European Union referendum vote when Cabinet colleagues were in opposing camps.
A Government spokesman said: "The Government remains committed to taking a decision on airport expansion and delivering additional runway capacity as planned by 2030. We will set out next steps in due course."
Shadow chancellor John McDonnell, whose Hayes and Harlington constituency would be hit if the Government decided to expand Heathrow, said any proposal for the site would be defeated in the courts because of the environmental concerns.
In July last year the Davies Commission recommended the building of a third runway at Heathrow, but the Department for Transport announced that further investigation into noise, pollution and compensation would be carried out before a decision is made.
David Cameron was expected to indicate which project would get the go-ahead after the EU referendum, but his resignation following the victory for the Brexit campaign meant the decision was left for his successor, Mrs May.
Tory former minister Grant Shapps said a free vote would be a "terrible" idea but insisted Mrs May was not likely to "fudge" the decision.
Mr Shapps, who leads the British Infrastructure Group of MPs, told BBC Radio 4's Today programme: "I don't believe it's something Theresa May would consider. This is the first big aviation decision she will be making, a massive infrastructure decision for Britain and it is not the kind of decision Thersea May would want to fudge or dodge - at least I hope not."