Theresa May has been warned to promote another Brexiteer into the Cabinet to keep the balance of her top team in the wake of Priti Patel’s dramatic departure.

The International Development Secretary, a prominent Brexit supporter, was effectively sacked on Wednesday for holding a string of unofficial meetings with senior Israeli figures without informing Downing Street.

The weakened Prime Minister is now facing pressure from pro-Brexit Tories to replace Ms Patel with another Eurosceptic MP and to retain the balance of her Cabinet, which would tip in favour of Remain after Ms Patel’s departure.

It comes after Ms May provoked outrage in her party by appointing former chief whip Gavin Williamson to replace Defence Secretary Sir Michael Fallon, who resigned last week amid allegations of sexual harassment.

Former Tory leader Iain Duncan Smith, an ally of Ms Patel, acknowledged that she had to resign and said the Prime Minister would want to retain “strong Brexit views” among her senior ministers.

He told BBC Radio 4’s Today programme: “It would be wrong therefore, I think in her own mind, to make any great changes to the balance of the Cabinet.

“I think we are all Brexiteers now, so the question is to what degree do you want someone in that job to be in support of David Davis and others, and I think therefore the balance on having strong Brexit views is one that in all probability the Prime Minister will certainly look for.”

Senior Tories told The Independent that the Prime Minister faces a “make or break” month to get a grip on her fragile administration, while questions marks still hover over a number of her top team.

Staunch Brexiteer Jacob Rees-Mogg said Ms Patel’s replacement must be someone who is “enthusiastic about Brexit”.

The Conservative backbencher told Channel 4 News: “I think the majority of Conservative members of Parliament are now both pro-Brexit in form and in meaning. 

“There are some who have a veneer of pro-Brexit about them but aren’t really. And there are a very small number who are deeply hostile. 

“But I don’t think it necessarily has to be someone who campaigned for Brexit. But it does have to be somebody who is now enthusiastic about Brexit. I think that’s correct.” 

Witham MP Ms Patel was forced to fly back from Africa for a confrontation with the Prime Minister on Wednesday after it emerged that she had held 12 meetings with Israeli figures including Prime Minister Benjamin Netanyahu during a family holiday in August.

She then held two additional meetings, one in the UK and one in the US, following her return from Israel.

Boris Johnson also faces questions over his future after he risked lengthening the jail sentence of Nazanin Zaghari Ratcliffe, a British woman imprisoned in Iran, by mistakenly telling MPs she had been “teaching journalists” 

Damian Green, Ms May’s de-facto deputy and close ally, and International Trade minister Mark Garnier both face Cabinet Office probes over allegations of inappropriate behaviour. Mr Green denies allegations against him.