Amber Rudd has exposed a Cabinet level rift after claiming it would be “unthinkable” for the Brexit negotiations to end without a deal – appearing to dismiss Theresa May's view that “no deal is better than a bad deal”.

Appearing in front of the influential Home Affairs Select Committee, the Home Secretary told MPs she believed it would be “highly unlikely” that Britain would crash out of the bloc but said her department was preparing contingency plans.

Asked by the senior Labour MP Yvette Cooper, who chairs the committee, whether Britain would be “as safe and secure” after Brexit with no deal in place, the Home Secretary replied: “I think it is unthinkable that there would be no deal.

“It is so much in their interests as well as ours – in their communities, families, tourists’ interests to have something in place. We will make sure there is something between them and us to maintain our security.“

Ms Rudd’s comments will undoubtedly be interpreted as a direct challenge to some of her colleagues. Last week the Prime Minister for the first time set out detailed plans on how the Government is preparing for Britain crashing out of the block without a deal.

Ms May also vowed to spend taxpayers’ cash immediately on preparing for a no deal, adding: “We are preparing for every eventuality. We are committing money to prepare for Brexit, including a no deal scenario.”

Just hours before Ms Rudd’s appearance David Davis, the Brexit Secretary, told MPs in the Commons that the maintenance of the option of no deal is for “both negotiating reasons and sensible security”.

“Any Government doing its job properly will do that,” he added.

Foreign Secretary Boris Johnson has also previously made the claim that Britain would be “perfectly OK” without a deal in place in March 2019 – the deadline for the negotiations in Brussels to conclude.

Referring to the Home Secretary’s comments to the committee, James Duddridge, a Conservative MP, posted on Twitter minutes later: “Far from being unthinkable, a no deal would be my preferred to achieve a fast, clean and boring Brexit.

“The sooner we get on with it the better,” he added.

Brexit: the deciders Show all 8 1 /8 Brexit: the deciders Brexit: the deciders European Union's chief Brexit negotiator, Michel Barnier Getty Brexit: the deciders French President Emmanuel Macron Getty Brexit: the deciders German Chancellor Angela Merkel Reuters Brexit: the deciders Commission President Jean-Claude Juncker EPA Brexit: the deciders The European Parliament's chief Brexit negotiator Guy Verhofstadt Getty Brexit: the deciders Britain's Prime Minister Theresa May Getty Images Brexit: the deciders Britain's Chancellor of the Exchequer, Philip Hammond PA Brexit: the deciders After the first and second appointed Brexit secretaries resigned (David Davis and Dominic Raab respectively), Stephen Barclay is currently heading up the position PA

After the Home Secretary's appearance a Downing Street spokesman said: "[Ms Rudd] is referring to the fact that a deal is in the best interests of both sides and that's something the PM agrees with."

During the two-hour session, the Home Secretary added that her department is expected to recruit an extra 1,200 staff by April in order to register the estimated three million EU nationals currently residing in Britain.

Despite repeatedly being unable to guarantee their status after Brexit in the event of a no deal, Ms Rudd said that she believed it would be “unthinkable” that EU citizens would be asked to leave Britain after March 2019.

She also insisted the Home Office was preparing “alternative plans” in case no security agreement was in place before Brexit.