Downing Street has slapped down Suella Braverman’s suggestion that she struck a deal with Rishi Sunak to lend him her support in exchange for key promises.

The Prime Minister’s press secretary rejected the former home secretary’s “characterisation” of a secret pact allegedly being reached, but confirmed the pair had been discussing policy prior to her Cabinet appointment.

In an incendiary resignation letter following her sacking on Monday, Mrs Braverman suggested she had given the PM her backing and served in his Government “on certain conditions.”

These included a commitment to cut net migration and efforts to override international barriers to deporting people who arrive in Britain via small boats in the English Channel, she said.

No 10 admitted that “something may have come in” when asked if Mrs Braverman had handed a document to Mr Sunak before her appointment.

Policy was discussed between the pair during the 2022 leadership contest, Downing Street suggested, adding it would be “quite odd” for them not to before she became home secretary.

But asked whether the PM and former home secretary had any kind of exchange in which a deal was struck before she entered Government, his press secretary said: “I do not accept that characterisation.”

“They obviously had a discussion on priority areas to work on and if you actually look at what we’ve worked on together with the Home Office during the last year, the toughest legislation on immigration, boats down by a third, crime falling, that would have been the basis of the ask for the home secretary, and obviously she would have had the opportunity to respond,” the press secretary said.

A reshuffle on Monday saw Mrs Braverman ousted and former prime minister David Cameron brought back as Foreign Secretary, with Mr Sunak hailing a new “strong and united team” in Government.

In a letter to the Prime Minister on Tuesday, Mrs Braverman – whose leadership ambitions are no secret – issued a rallying cry to the party’s right with a call for an “authentic Conservative agenda”.

The former minister claimed she had agreed a deal to back Mr Sunak and serve as home secretary “on certain conditions”, such as introducing measures to override the European Convention on Human Rights (ECHR) and the Human Rights Act (HRA) in legislation to stop small boats crossing the Channel.

“You have manifestly and repeatedly failed to deliver on every single one of these key policies,” she wrote, adding: “Either your distinctive style of government means you are incapable of doing so. Or, as I must surely conclude now, you never had any intention of keeping your promises.”

She accused him of a “betrayal of your promise to the nation that you would do ‘whatever it takes’ to stop the boats” and said his response to the pro-Palestinian protests showed he is “uncertain, weak, and lacking in the qualities of leadership that this country needs”.

In a brief response, a No 10 spokeswoman said the Prime Minister “believes in actions not words”.

“He is proud that this Government has brought forward the toughest legislation to tackle illegal migration this country has seen and has subsequently reduced the number of boat crossings by a third this year. And whatever the outcome of the Supreme Court tomorrow, he will continue that work,” she said.

“The PM thanks the former home secretary for her service.”