Amber Rudd has refused to rule out resigning from the cabinet if Theresa May decides to pursue a no-deal Brexit.

The work and pensions secretary said she was "committed" to ensuring that the UK does not crash out of the EU without an agreement.

As ministers clash over the government's "plan B" for Brexit, she refused three times to say she would stay in the government should Ms May decide to settle for no deal if MPs vote down her proposed agreement next week.

The Commons is widely expected to reject the deal, with one BBC projection suggesting the government could lose the vote be a margin as big as 228.

Cabinet ministers are split on how the government should respond if the vote is lost. Some are pushing for a no-deal exit while others insist this would be disastrous for the country and instead want the prime minister to opt for a softer Brexit.

Asked whether she agreed with the foreign secretary, Jeremy Hunt, that the UK would "thrive and prosper" if there was a no-deal Brexit, Ms Rudd told BBC Radio 4's Today: "This is a strong and great country, we will find a way to succeed, but I do not think that no deal would be good for this country and I'm committed to making sure that we find an alternative."

She said it was "right" for the government to make preparations for a no deal, comparing it to "having a seatbelt on when we're driving a fast car".

But she said: "I intend to work with colleagues to make sure we avoid it. I am committed to getting the best outcome for this country, which is supporting the prime minister's deal."

It comes after Greg Clark, the business secretary, also suggested he could resign if the government opts for a no-deal Brexit, while David Lidington, Ms May's deputy, said such an outcome would cause "irreversible damage".

He told the Commons: "I oppose a no-deal exit not just because of the economic harm but because I actually believe that a no-deal exit would cause profound and possibly irreversible damage to the Union of the United Kingdom. The tensions in Northern Ireland and in Scotland resulting from such an outcome would be severe."

Police separate clashing Brexit protesters outside Parliament Show all 11 1 /11 Police separate clashing Brexit protesters outside Parliament Police separate clashing Brexit protesters outside Parliament Anti-Brexit protester Steve Bray (left) and a pro-Brexit protester argue as they demonstrate outside the Houses of Parliament Getty Images Police separate clashing Brexit protesters outside Parliament A pro-Brexit protester argues Getty Images Police separate clashing Brexit protesters outside Parliament Police surround the pro-Brexit protester after he confronted Steve Bray, a pro-European protester Getty Images Police separate clashing Brexit protesters outside Parliament A leave supporter is spoken to by a police officer as he argues with a remain supporter, Steve Bray, outside Parliament PA Police separate clashing Brexit protesters outside Parliament MPs in Parliament are to vote on Theresa May's Brexit deal next week after her December vote was called off in the face of a major defeat Getty Images Police separate clashing Brexit protesters outside Parliament A leave supporter is spoken to by a police officer PA Police separate clashing Brexit protesters outside Parliament Police look on as anti-Brexit protesters demonstrate outside the Houses of Parliament. Getty Images Police separate clashing Brexit protesters outside Parliament Police hold back a leave supporter PA Police separate clashing Brexit protesters outside Parliament A police officer speaks with anti-Brexit protester Steve Bray Getty Images Police separate clashing Brexit protesters outside Parliament Police surround a pro-Brexit protester after he confronted a pro-European protester Getty Images Police separate clashing Brexit protesters outside Parliament Conservative MP David Davies, wearing a gopro camera, speaks to anti-Brexit protester Steve Bray Getty Images

The public sparring between rival ministers, many of whom are eyeing up Ms May's job after she was forced to say she will not fight the next general election, has infuriated No 10.

Robbie Gibb, the prime minister's director of communications, wrote to government special advisers to tell them to stop quietly campaigning on behalf of their ministers.

In a letter seen by the Daily Mail, he wrote: "No 10 worked incredibly hard and deliberately starved out the Downing Street weekend grid to give the launch of PM's NHS plan - its biggest ever cash injection - the best possible coverage.

"But because of briefings and articles by ministers in Sunday papers, attention was diverted elsewhere. To add to our frustration, No 10 had no warning of two ministerial op-eds and there was a briefing on a policy change we did not approve."

Insisting that "the situation cannot continue", he added: "Let me remind you that all government special advisers work for the prime minister as well as your own secretary of state. Your duty is to promote the government's message, not just your own minister's."

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Ms Rudd also confirmed that she will scrap the retrospective two-child limit for people on Universal Credit. The policy restricted benefits to a recipient's first two children, even if they had exceeded the limit before the policy was introduced.