Tory leadership hopefuls have “stepped up a gear” in making their pitches to replace Theresa May as pressure mounts on the prime minister to set a date for leaving Downing Street.

Rivals have undertaken a flurry of activity both behind the scenes and in the media as speculation grows that Ms May will announce her departure in the coming weeks.

The expectation has been fuelled by signals that Conservative MPs whose votes the prime minister desperately needs to pass her Brexit deal would back her plan if she sets out her departure schedule.

With senior Tories such as Priti Patel, Liz Truss and Dominic Raab all making public interventions within days of each other and following a tumultuous week in parliament, even Downing Street aides have accepted the political reality that Ms May’s authority has faded.

It comes as the prime minister prepares for what might be her final attempt to push her twice-defeated Brexit deal through the House of Commons on Tuesday, with her team holding talks to win round DUP, Eurosceptic Tory and Labour MPs.

Priti Patel, former international development secretary (AFP/Getty)

As discussions continue on Monday, one potential leadership contender, ex-cabinet minister Priti Patel, will appear on stage at an event organised by a right-of-centre think tank.

One MP told The Independent: “To all intents and purposes it looks like Priti is putting herself out there just as the wheels fall of the PM’s wagon.

“She knows she’s from the right part of the party, the part which is going to chose the next leader, so she’s reminding everyone she’s there.

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“For all anyone knows Theresa will have announced when she’s off within the next couple of weeks. So all the wannabes have stepped up a gear.”

Friends of the senior MP, who was involved in the Vote Leave campaign, said the event was not part of a leadership push, had been organised sometime ago and would focus on international development only.

But it is likely to at least give Ms Patel a platform to talk about Brexit, her values, the future of the country and the prime minister’s troubled withdrawal agreement, which she has consistently voted against.

Others have indicated that Ms Patel could become a running mate for Boris Johnson, the perennial leadership contender, who polling shows is still among the most popular choices of Conservative members.

On Saturday another hopeful, chief secretary to the Treasury Liz Truss, gave a lengthy interview to The Times in which she set out radical policies on the social mobility agenda, like Oxford and Cambridge universities taking 100 of the brightest state-school pupils from every area.

Asked if she would like to run for leader she said: “I think the Conservative Party spends far too much time talking about personalities and not ideas.

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“It’s never wise to rule out anything in politics, but I’m absolutely not thinking about it.”

Pushed on whether she would be a running mate for a male candidate, she added: “I don’t want to be the number two.”

Ex-Brexit secretary Dominic Raab, fast being seen as the strongest Brexiteer rival to Mr Johnson, dropped a further hint that he will run, after making a major speech on social mobility a few days earlier, he said: “Never say never.”

Dominic Raab, former Brexit secretary (AFP/Getty) (AFP)

A senior Tory Leave-backing MP said: “Dominic is very active right now. He’s the one to look our for.”

Leading contenders Sajid Javid, the home secretary, and foreign secretary Jeremy Hunt are both said to have operations ready for a tilt at the top job.

But they will have to overcome the fact that they voted to extend Article 50 earlier this week, another Conservative linked to the Brexit-backing European Research Group (ERG) said.

He added that former Brexit secretary David Davis’s chances of reviving his leadership hopes had crumbled due to how he announced he would vote for Ms May’s deal during the week.

He said: “His reputation is f***ed in the ERG. He can forget about running for the leadership.”

On Friday, it emerged that chancellor Philip Hammond is leading government talks with the DUP in a bid to win their support for Ms May’s deal, prompting speculation there could be financial incentives for the party to back the plan.

The Independent also revealed talks between government officials and Labour MPs to enshrine in law parliament’s ability to share the future relationship in return for backing her deal.

DUP Nigel Dodds says talks over Brexit deal will continue over the weekend

While some Conservatives who had opposed it in the first instance are changing their minds, it is not yet enough to win the vote.

It was reported on Saturday that close aides now believe the only way she can gain a majority for her deal will be announcing she is standing down by October’s Conservative Party conference.

A Tory Brexiteer echoed the view, saying: “For some people, even in that hardcore group of the ERG that No 10 finds difficult to reach, it does change things.

“She would need to stand at the despatch box and say I’ll be gone by X date.

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“Self-interest alone would have some affect. With her quitting on the cards, do you not think Sajid [Javid] and Jeremy [Hunt] will be saying to their mates, ‘that’s what you should be calling for to back the deal’?”

If the meaningful vote on Ms May’s deal is won on Tuesday then she will head to the European Council summit on Thursday calling for an extension of the Article 50 period until 30 June, in order to pass necessary legislation to complete Brexit.

If not then the EU is unlikely to grant an extension without knowing what it is for, with growing pressure from Brussels to either join a customs union or call a new referendum.