Sir Keir Starmer and his backers argue a leadership contest would paralyse the government for months.
There is a big moment coming in the next 24 hours, for Sir Keir Starmer and for would-be challengers to the prime minister.
BBC correspondents look at some of the new bills Sir Keir Starmer's government wants to pass.
The monarch has outlined the government's plans for new laws in the next session of Parliament.
Health Secretary Wes Streeting leaves No 10 less than 20 minutes after arriving for a meeting with the prime minister.
Ministers including Safeguarding Minister Jess Phillips have resigned over Sir Keir Starmer's leadership.
The prime minister told the Cabinet a leadership contest had not been triggered, and that he wouldn't be resigning.
The economic crisis is the main item on the agenda for today's cabinet meeting, which takes place away from London for the first time since the 1920s.
Labour rebel Frank Field is expected to join forces with former Conservative minister Nicholas Soames to call for a cap on the number of immigrants settling in Britain.
David Cameron has said a Conservative government would introduce tax cuts to reward those who "put their backs into the British economy".
Ministers have expressed anger and regret over the loss of a computer disc containing personal details on thousands of justice staff.
Labour must take more effective action to help people cope with the economic downturn or face electoral defeat, the TUC leader has said.
Labour must take more effective action to help people cope with the economic downturn or face electoral defeat, the TUC leader has said.
The Green Party is set to elect its first leader, with Caroline Lucas favourite for the role.
Scotland's finance secretary has accused Gordon Brown of "caving in" to the case for more powers for the Scottish Parliament.
David Cameron has the power to kill the Lisbon Treaty "stone dead", the leader of the United Kingdom Independence Party has said.
An inquiry chaired by Cherie Booth has denounced the "hysterical rhetoric" of politicians trying to satisfy the "public clamour for prison-based punitiveness."
The prime minister has signalled that the government will not give a one-off payment to help poorer households meet rising fuel costs.
A senior Conservative has said that the Tories must begin to make detailed plans for governing.
The Liberal Democrats have called for minor criminals to be kept out of jail.