Stick to Brexit script on immigration, David Davis told

The deepest cracks so far have emerged in Theresa May’s Cabinet over Brexit – as Downing Street distances the Prime Minister from the man she has appointed to oversee secession from the EU.

A Number 10 spokesperson said David Davis’s claim that it was “very improbable” Britain would stay in the European single market was “his opinion” – and not policy. The Secretary of State for Exiting the European Union on Monday told the House of Commons that if border controls were not allowed within the single market the UK would most likely leave it.

When pressed at a briefing however, the Prime Minister’s spokesperson denied that Mr Davis’s take on the matter was official policy – but presented no clear picture about how the Government would actually proceed. Asked whether Mr Davis was speaking for the Government, the Downing Street spokesperson said the statement was the minister’s opinion and that there were “differing views” on the subject. “Saying something is improbable or probable I don’t think is necessarily policy,” she said.

“He said it was improbable; he’s setting out his view that it’s improbable. The Prime Minister wants to have the work underway – she recognises that people have their differing views and that’s why we need to do the work that there is. All of this is going to have to be negotiated with our European partners and the Prime Minister’s view is that we should go after the best deal we can.” The comments from Downing Street suggest Ms May has not completely given up hope of keeping Britain in the single market. She and those around her have however been coy about what Brexit would entail – frequently deploying the ambiguous slogan “Brexit means Brexit”.

One area Ms May has weighed in is confirm that she would not be in favour of a points-based immigration system as pledged by top Leave campaigners, including Boris Johnson, during the EU referendum campaign. The spokesperson declined to elaborate on the sort of immigration controls Ms May would advocate instead. “I think what you’ve seen is her talking about a system that wouldn’t work,” she said. Mr Davis, who was appointed to head the new Department for Exiting the European Union by Ms May, on Monday afternoon told the Commons: “This Government is looking at every option but the simple truth is that if a requirement of membership is giving up control of our borders, I think that makes it very improbable.”

The hasty caveating of Mr Davis’s comments by Ms May’s official spokesperson is not the first time she has come to blow with hardcore eurosceptics in her Cabinet. On a trip to the United States, International Trade Secretary Liam Fox said the Government would most likely seek a free-trade agreement with the EU rather than a closer “customs union”. Downing Street once again waded in by saying no decision had been made on which way forward the UK would take.