As allies defend prime minister, some MPs fear her much-criticised handling of the tower block tragedy could be her undoing

Concern is growing within the Conservative party over Theresa May’s handling of the Grenfell Tower fire, with some fearing it could become “her poll tax moment”.

Several of the prime minister’s allies defended her response to the tragedy on Saturday after she was criticised for her initial failure to meet residents and stilted interviews that left many questions unanswered.

They said there was an unfair narrative that did not reflect efforts she had been making behind the scenes. “There is a story out there and facts are selected to fit it,” said one.

There is concern, however, among Tory MPs that the disaster has again placed the spotlight on May’s difficulties in demonstrating empathy and responding on her feet, weaknesses that were exposed during the election campaign.

Facebook Twitter Pinterest Protest posters at a rally in Whitehall on Saturday. Photograph: Jonathan Brady/PA

“It is an extraordinary tragedy and there will be a lot of questions to ask, but I can’t help feeling that in some people’s minds this might be her poll tax moment,” said one former minister. “You can see real anger.

“Labour may not be able to form a government without an election, but they could get people out on the streets. We have a really difficult problem inside the Commons and tough times with this sort of emergency coming up outside.”

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Margaret Thatcher’s plan to introduce the poll tax, officially called the community charge, was eventually abandoned following riots in 1990.

Another Tory MP compared May to Gordon Brown, whose mechanical style and insistence to be across all detail allowed him to be a successful chancellor but did not translate well once he was prime minister.

“She is a bit like Brown. What appear to be her strengths actually contain her weaknesses as well, and she finds it very difficult to publicly display her emotions,” the MP said. “That is not to say she doesn’t have a sense of humour or that she can’t cry. But she is adrift at present.”

After the shock of the election result and the Grenfell disaster, May now faces a difficult week that will also see the government announce a stripped down Queen’s speech, with plans to introduce new grammar schools, change the education funding formula and cut winter fuel payments expected to be ditched or diluted.

There is a febrile atmosphere inside the parliamentary Conservative party. There is little appetite for an immediate leadership challenge or an election, which many MPs are convinced they would lose, but MPs believe it could soon become obvious that the party has no scope to pass significant new laws.

With May now more damaged than ever, they fear the Conservative party conference will be the stage for an “October beauty contest” to select a new leader.

“It is almost overwhelming,” said one Tory MP. “Things are changing so quickly. The assumption is Theresa May has weeks or months. William Hague’s definition of the Tory party was that it was an autocracy tempered by regicide. I think if you look back over 150 years, that is exactly so.”

The departure of May’s joint chiefs of staff, Nick Timothy and Fiona Hill, in the wake of the election has also left the prime minister without her two most trusted advisers. Some Tories are convinced she is still in touch with the pair.

The two most important people in the operation now are “the two Gavins” – the chief whip, Gavin Williamson, and May’s new chief of staff, Gavin Barwell, who lost his Croydon Central seat at the election.

Allies of Boris Johnson have been making clear that he has no intention of trying to topple May, warning his supporters against making any indication that he is on manoeuvres.

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“For lots of reasons, the last thing the parliamentary party wants at the moment is a leadership contest,” said an MP. “It might be Boris, it might not be Boris, but taking two or three months doing that now would not be good. And it could still mean a general election and there is a good chance we would lose it.”

Others in the party believe May’s immediate task is simply to navigate a hard week that includes dealing with the Grenfell fallout, the beginning of Brexit talks, finalising a confidence deal with the DUP and the Queen’s speech.

“She has never been as low, but I wouldn’t underestimate her concept of public service and her determination,” said one party veteran. “There is a sizeable proportion of the cabinet who are prepared to bolster her as much as possible.”

Another MP was less optimistic: “The next six weeks will show we can’t do very much. It may be she lasts a bit longer, but it will be a sheer grinding down. People will be fed up with impotence.”