Theresa May doesn’t want to be compared to an animal. On her flight to China on Tuesday evening, the Prime Minister was asked about the unflattering description by one of her MPs, Robert Halfon, that her premiership and policymaking was more like a tortoise than a lion – painfully slow rather than magnificent and bold.

“I have never tried to compare myself to any animal, or bird or car or whatever sort of comparisons that sometimes people use,” she said.

Unfortunately for her, this comment by Halfon hit the nail on the head for many Conservative MPs who are unhappy with May’s leadership. Besides the ongoing rows within the Tory party over Brexit, the second-biggest talking point is the lack of ideas emanating from No 10. Planning grids are sparse with announcements, while big policy challenges are put off on the pretext that Brexit needs to be tackled first.

Given that the process of withdrawal from the EU, including the transition phase, is going to take at least two more years, this is alarming. Mrs May even wants to put off the much-needed refurbishment of the Unesco World Heritage fire risk that is the Houses of Parliament, debated by MPs on Wednesday, in case it gets in the way of Brexit.

May’s style of governing is not so much the behaviour of a tortoise but an ostrich. Faced with something so huge and unwieldy as Brexit, she cannot seem to trust her Brexit Secretary, David Davis, with taking the full mental burden for this challenge. As a result, she refuses to focus on the other major problems the Government must deal with: the NHS, social care, housing, welfare and the cost of living. On these, it is head-in-the-sand time.

As she flew into China, May dismissed talk of a leadership crisis by insisting: “I am not a quitter.” This is her favourite line when asked about her own troubles as Prime Minister – she used it last summer during a similar storm. It conveys, she hopes, a woman who is selflessly getting on with a job of work for the good of the country rather than skipping off like her predecessor David Cameron. This is an admirable quality, but it is worth little if she refuses to engage with the deeper, structural problems with her premiership.

Aboard her flight, May did admit she needs to communicate better with her MPs, which may settle some of the more excitable members who are thinking of writing to Sir Graham Brady, chair of the 1922 Committee, who will call a vote of confidence if and when he gets to 48 names. But it will settle them only temporarily.

When it comes to communication, May has only a marginally easier time getting her point across than Wikie the talking killer whale. During last year’s election, when trying to portray herself as strong and stable, and armed with what should have been a sensible policy that restored some fairness to the social care system, May failed to communicate authority and competence to the electorate.

This inability does not just apply to conveying to voters what her plans are for government as this decade draws to a close, but to her MPs in the Commons tea rooms. Famously bad at social networking – real social networking with a glass of wine or a cup of tea, because nobody expects her to be good at Twitter – May has to be almost dragged into the Commons to take the temperature of her parliamentary party. Is she ever in listening mode? Many of her MPs don’t think so.

This failure to listen would be difficult for any Prime Minister, but at times of crisis her personal shortcomings are amplified. What was seen as dogged determination when she was on a high a year ago now seems like stubborn mulishness. When she arrived in No 10 in July 2016, she promised to speak up for the just-about-managing, the people who struggled to make ends meet and who had felt cut off from Westminster. But 18 months on there is little evidence to show of real policies from her Government to help those facing what she described as “burning injustices”.

Unsurprisingly, a YouGov poll this week suggested one in five people who voted Conservative last year think she should now stand down as Prime Minister. With the local elections coming in May, this figure will alarm many Tory MPs.

Taking a prime ministerial foreign trip while critics are circling was always going to be dangerous. It is telling, and ironic, that her visit to China was scheduled for last summer but had to be delayed. Yet one thing she cannot delay is tackling the crisis in her leadership – otherwise the only animal she will be compared to is a lame duck.

The Independent