Senior Conservatives said both ministers had committed sackable offences which had materially damaged the UK’s interests and those of its citizens.
The furore around Ms Patel’s unofficial trip to Israel grew, as it emerged she may have omitted to tell Ms May she discussed funnelling UK aid cash to the country’s army despite Downing Street asking for full details of her visit.
Foreign Secretary Mr Johnson tied himself in knots in the House of Commons, denying he made comments that were clearly recorded in Parliament and which led to the Iranian judiciary threatening to double a British woman’s prison sentence.
The twin ministerial gaffes come less than a week after the Prime Minister pushed Sir Michael Fallon out of her Cabinet, following allegations about sexually inappropriate behaviour, but then damaged her already weakened authority and angered MPs by appointing a loyal lieutenant to replace him with little ministerial experience.
It first emerged on Friday that International Development Secretary Priti Patel, often talked of as a future Tory leader, had a string of meetings with Israeli politicians – including Prime Minister Benjamin Netanyahu – while on holiday without telling Downing Street.
A senior Conservative told The Independent: “Ministers must uphold collective responsibility and mustn’t engage in activity that undermines the collective work of the Cabinet.
“Ministers may always meet people by chance, but you should always keep the Government informed. You don’t allow yourself to do be pulled into a major programme of tours and meetings, particularly which impact on your official role.”
The Tory MP added: “If the Prime Minister wanted to sack a minister for this kind of thing she could.”
Ms May only found out about Ms Patel’s trip months later, and on Monday censured her at a meeting at which the minister was told to set out everyone she had met and what had taken place.
It then emerged on Tuesday that the ambitious cabinet minister discussed possibly funnelling UK aid cash to the Israel Defence Forces, to support Syrian civil war refugees arriving in the Golan Heights where the IDF has a field hospital.
But Downing Street could not say the idea, already condemned by the Palestinian authorities, had been revealed to Ms May at the “tell all” meeting the day before.
Asked whether Ms Patel would face further censure, Number 10 drew a line under the matter, saying it was not clear if the International Development Secretary had breached the ministerial code and that the code would be reviewed to iron out any ambiguity.
An urgent question was called on the affair in the Commons, but Ms Patel failed to show as she had another trip to Ethiopia, leading Labour and other opposition parties to vent their anger.
Shadow International Development Secretary Kate Osamor said Ms Patel should do “the decent thing” and resign, saying: “It is hard to think of a more black and white case of breaking the code of ministerial conduct. Rather than changing the minister, the Prime Minister has decided to change the ministerial code.”
The Lib Dem spokesman Shas Sheehan said: “[Ms Patel] has forfeited the respect of colleagues and officials and should go.”
In the Commons, Tories held off overtly calling for Ms Patel’s head, with former Foreign Affairs Select Committee chairman Crispin Blunt telling one of her junior ministers he should “take her very gently in hand” and sort the situation out.
Mr Johnson, meanwhile, found himself furiously backpedalling over comments he made about Nazanin Zaghari-Ratcliffe.
The 38-year-old British woman was arrested and jailed in Iran, accused of spreading propaganda, with a central part of her defence being that she had never worked teaching journalists in the country, but was merely there on holiday.
But when Mr Johnson mistakenly told MPs in a public hearing that she had been teaching journalists, Ms Zaghari-Ratcliffe was hauled in front of an Iranian court and threatened with another five years in prison – on top of her existing five-year sentence.
In a bid to defend Mr Johnson’s gaffe, fellow cabinet minister Liam Fox said his words were akin to “slips of the tongue” that anyone can make.
But a senior Conservative backbencher told The Independent: “Johnson should go.
“How could he be so cavalier with his words when the freedom, health and sanity of a British national is at risk.
“I felt ashamed listening to Liam Fox trying to defend him.”
Conservative former minister Anna Soubry said on Twitter that in “normal times”, Mr Johnson would have been sacked.
She added: “The lack of contrition is as shameful as the original error. Boris Johnson doesn’t understand magnitude of the job & responsibility he holds.”
Mr Johnson made a phone call to his Iranian counterpart in a bid to repair the damage, and argued that in the original committee he had been making a wider point about how it was wrong to arrest anyone for teaching journalists.
He told MPs he is sorry if his remarks about a British woman jailed in Iran had been “so misconstrued” to have caused anxiety to her family.
But the Foreign Secretary stopped short of meeting repeated requests to admit he made a mistake and offer an unequivocal apology.
Downing Street said Ms May still had “full confidence” in him, with Ms May’s official spokesman saying: “The Foreign Secretary is doing a good job and working hard to represent Britain’s interests abroad.”
But the lack of action against either minister only served to underline the difficulty of Ms May’s position.
Having lost Sir Michael last week, two further ministers, Damian Green and Mark Garnier, face Cabinet Office investigations over inappropriate behaviour.
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