There are stories of an imminent leadership challenge, but senior Tories have dismissed the notion, and there is no obvious successor

Theresa May will face parliament this week reasonably confident that speculation about an imminent leadership challenge remains unfounded, but knowing that her long-term credibility with her party has been damaged beyond repair.

The concept of a “worst week ever” is something of a cliche for political leaders, but few have seen their stock plummet so quickly as May’s did in the period between Friday 9 June, when she realised her early election gamble had backfired, and the following Friday when crowds, angry at her supposedly unsympathetic response to the Grenfell Tower tragedy, yelled “coward” at her as she was driven away from a meeting with victims encircled by police for her protection.

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The newspapers over the weekend carried stories saying that May is facing a “stalking horse” leadership challenge, or that she has been given just “10 days to save her premiership”.

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But the idea that May is facing an imminent leadership challenge is being dismissed as hyperbole by senior Tories. One MP who would expect to be aware of a plot if there was one said he was “mystified” by the reports and No 10 does not believe that a coup is imminent.

The Sunday Telegraph said that Tory Eurosceptics were preparing to launch a leadership challenge in the event of May watering down her plans for Brexit. But the European Research Group, the influential and well-organised caucus pushing for a relatively hard Brexit, is said by one source to be “absolutely solidly behind Theresa”, not least because the Brexiteers are worried that if May were to go, she could be replace by someone more pro-remain.

On Wednesday, May will have to deliver a major speech at the start of the Queen’s speech debate, and the crunch will come when MPs come to vote on it about a week later. But, for all the speculation about this being a make-or-break moment, Downing Street is very confident of winning the vote and, with the DUP expected to vote with the Conservatives, May should get her Queen’s speech through with a majority of around 13.

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May took steps towards restoring her post-election reputation with her party last week by giving a sincere and contrite speech to MPs at the backbench 1922 Committee, but since then the Grenfell Tower tragedy, along with her apparently tardy and emotionally wooden public responses, have renewed fears in the party that she is temperamentally unsuited to be prime minister.

“It has underlined that Theresa is aloof, impersonal, and finds it difficult to empathise,” said one backbencher. “She has not reacted in a way that would have come easy to Tony Blair or David Cameron.”

Some of those that work with May accept that she just does not connect emotionally with people in the way that other politicians do. But they also believe that some of the criticism levelled against her over Grenfell Tower has been “outrageous”, saying that when she met firefighters, not victims, on the Thursday she was following precedent and acting on the best advice of her security team.

May’s plight is highlighted by YouGov favourability polling figures published on Wednesday. In April, May had a net favourability rating of +10 (those who say they have a favourable opinion, minus those who say they have an unfavourable opinion), while the Labour leader, Jeremy Corbyn, languished on -42. But now he is up to 0, and May’s ratings have collapsed to -34.

Much as the Conservative party might like to replace May with a popular and dynamic leader, the key problem remains, as one MPs put it, “that there’s no obvious successor”. Unless May were to resign, a leadership contest would only happen if 15% of Tory MPs – 48 of them – write to the chairman of the 1922 Committee demanding one, and there is no evidence that anything like that number are in favour.

Boris Johnson, the foreign secretary, is the most high-profile potential candidate and, unlike some of his rivals, he does have the remnants of a campaign team that could be activated on his behalf. But, mindful of what happened when his predecessor as MP for Henley, Michael Heseltine, challenged Margaret Thatcher, he is acutely aware that disloyalty gets punished in the Conservative party and has been urging MPs to get behind May.

It is also unclear how any successor could shift party policy on Brexit – or, indeed, anything much else – without triggering a damaging party split. May’s premiership could still have some time left to run.