BORIS Johnson could resign and potentially spark a Tory leadership race if Theresa May opts to pursue a ‘Swiss-style’ soft Brexit, it emerged yesterday.

As tensions within the Cabinet escalated it was revealed that, despite publicly denying he will quit the Tory frontbench, speculation persisted that he would do so.

The Foreign Secretary told reporters in New York he would not resign and denied that ministers were split over Brexit policy, insisting: “We are a nest of singing birds.”

Further reports suggested Johnson would consider it a matter of resignation if May veers towards the kind of soft-Brexit relationship advocated by Chancellor Philip Hammond when she makes a key speech in Florence on Friday.

It emerged yesterday that the Foreign Secretary could even quit before the weekend if May signals she will agree to the UK paying for access to the single market permanently, in an arrangement similar to staying in the European Economic Area (EEA).

This option is similar to the arrangements adopted by Switzerland, known by its critics as the “EEA-lite”, but would be a way of preserving the benefits of the single market.

Friends of Johnson told a newspaper yesterday he “could not live with” the version of Brexit under consideration, which prompted the publication of his personal vision for Brexit on Saturday.

His article was widely regarded as a warning shot to the prime minister over a potential leadership challenge as she prepares to deliver her crunch Brexit speech.

May’s speech is expected to focus on the transitional period after March 2019, and to moot the idea of a “pay to play” deal, where the UK would pay for access to the single market and customs union.

But the Foreign Secretary – who appears to have the backing of other pro-leave ministers, including his EU campaign ally Michael Gove – was unhappy about some of the expected wording in the speech.

He is said to be opposed to a close long-term relationship with the rest of the EU along the lines of Norway or Switzerland – with more leeway over freedom of movement – and which may be put forward by May.

Johnson and others fear that would limit the UK’s ability to do deals with other countries, and require the UK to mirror EU regulations too closely. His newspaper article signalled that he could not support such a relationship.

Johnson and May are both in New York for the UN General Assembly, but it was reported that they have not met since his article was published, despite staying in the same hotel.

Some senior Conservatives believe Johnson should have been sacked for undermining May’s authority. Former chancellor Ken Clarke said Johnson should have faced the sack for his Brexit intervention, while William Hague warned that if Cabinet rows continued Labour’s Jeremy Corbyn would become prime minister.

Clarke said: “Sounding off personally in this way is totally unhelpful and [Johnson] shouldn’t exploit the fact [May] hasn’t got a majority in Parliament, and he knows perfectly well that normally the Foreign Secretary would be sacked for doing that – and she, unfortunately, after the General Election, is not in the position easily to sack him, which he should stop exploiting.”

May, who could leave herself vulnerable to a leadership challenge if she sacked Johnson, has indicated she expects him to continue in the Cabinet. Asked if the PM thought he would remain as Foreign Secretary, her spokesman said: “Yes. Boris Johnson is the Foreign Secretary and, as the Prime Minister has said, he is doing a good job.”

Friday’s speech is expected to be the most important update since May’s Lancaster House address in January and is thought to include an attempt to break the deadlock over the “divorce bill”.

It has been suggested she will offer to pay tens of billions of pounds to the EU during a two to three-year transition deal after the formal exit in 2019.

Johnson is understood to accept the UK paying its dues during a transition period, but not continued payments for access to the European single market on a permanent basis.