The fragile cabinet truce over Europe was already fracturing on Saturday night as allies of Boris Johnson declared that the foreign secretary had forced the prime minister to alter her crucial Brexit speech.

In claims that infuriated Downing Street, supporters of Johnson were claiming that he had successfully stopped Theresa May backing the so-called “Norway option”, under which Britain would continue to have access to the EU’s single market in return for payment and adherence to its rules and regulations.

They also claimed that he had stopped the prime minister from adopting a far longer transitional period of up to five years, and accused Philip Hammond of attempting to push May into adopting a four-year transition period. Treasury attempts to impose such a measure had been frustrated with Johnson’s help, his supporters claimed.

Allies of the chancellor were adamant that Hammond had been pushing no such plan, pointing out that he had been publicly advocating a transition period of two or three years at the most.

The infighting signals the near-breakdown of the Tory truce over Brexit just a week before the party conference in Manchester – and is another sign that May is struggling to maintain discipline in the wake of her disastrous election result. In a new twist, the Sunday Times claimed that Hammond had texted Johnson after the Tories lost their majority, suggesting he would back the foreign secretary should he decide to run. A source close to the chancellor told the paper: “I’m not going to quibble with that.” Another said they “did not recognise” the account.

Senior Tories are now concerned that Johnson could leave the cabinet at any moment, though May has so far declined to dismiss her foreign secretary. Some think Johnson is attempting to become a “Brexit martyr” by earning the sack.

The skirmishes also expose the serious tensions that exist between Hammond and Johnson, with both men seen as potential future leaders. May had appeared to win temporary unity among senior Tories by using her speech in Florence last Friday to say that Britain wanted to leave the EU’s single market and customs union, but only after a two-year transition period during which payments would continue to Brussels.

Downing Street denied the claims that Johnson had secured changes to May’s speech, with senior government sources insisting that the prime minister had never considered a four- or five-year transition period and that Johnson’s intervention had not caused her to rule out a Norway-style deal.

May has always been clear that you can forget the Swiss model, or the Norway model, or any other model Conservative source

“She has always been clear that you can forget the Swiss model, or the Norway model, or any other model – we are going for a bespoke deal,” said a source. They would concede only that Johnson had been influential in ensuring that May “slightly turned up the positivity dial” in her address.

The claims of victory from Johnson’s supporters come after he reopened the Tory row over Europe last weekend, writing a 4,000-word essay on his own vision for life outside the EU. Supporters claimed that before his intervention, the government had been heading for a future in which Britain would have been out of the EU “in name only”.

While May’s speech was given a cautious welcome by the European commission, hopes are not high in the UK government about an immediate breakthrough in Brexit negotiations. Despite concessions made by the prime minister over paying into the EU pot during a transition period, several government insiders said they believed that Brussels would not agree to talks over a future trade deal next month. Instead, insiders now hope the talks will begin before Christmas.

Meanwhile, there are concerns among some in the cabinet and in the Tory ranks that not enough work is being done to prepare for the possibility of crashing out of Europe with no deal.

The former cabinet minister Oliver Letwin was appointed after the EU referendum by David Cameron, then prime minister, to lead the Whitehall unit charged with preparing to leave the European Union. Letwin told the Observer: “My sense is that the work is beginning inside government now, but I don’t believe it has yet reached anything like the level of intensity that it needs to reach. That is OK – there is still time, but it will have to be done in the next few months, because that is detailed work and it is implementation work. It requires clear thinking and administrative competence.”