It’s that time of year again: the Tory party is attempting a detox. This week the prime minister’s chief of staff, Gavin Barwell, called Conservative MPs into a meeting and informed them they were all going to be much more caring from now on. According to a briefing document seen by the Guardian, they will be caring more about housing, schools, and tackling injustice – but most of all they will be caring about the environment, and all the animals who live there.

You can see why such an intervention is needed. The party has of late been on a particularly unwise bender when it comes to seeming not to care about animals. And this in Britain, a country with a proud history of sending its eight-year-olds down mines, up chimneys and to grim boarding schools – all the while sobbing uncontrollably should a pet dog get ill.

Last week a bungled announcement about animal treatment led to fake claims that the Tories had ditched recognition of “animal sentience” in UK law. This came after the prime minister omitted ivory bans from her manifesto, and then proceeded to announce a free vote on foxhunting. (A Tory source says letters MPs get from constituents concerned about foxes outnumber those they get about Brexit at a ratio of 13 to one.)

So a spell in rehab is in order. This is nothing new. The Tories have been in and out of this situation ever since William Hague took a ride on a log flume wearing a baseball cap with HAGUE on it, in an attempt to make his party look modern. Since then the Conservatives have tried cycling to parliament, hugging a hoodie, driving a dog sled across the Arctic, changing their logo to an oak tree, and claiming that GWB (general wellbeing) is as important as GDP (gross domestic product). They have marketed themselves, variously, as the “greenest government ever”, “compassionate Conservatism”, and the “workers’ party”. They are now, inevitably, the rebrand party.

But when someone – let’s say, for the sake of argument, a drug-addled celebrity in the early 2000s – announces they are going on a detox every six months, it isn’t usually a sign that the detoxes are working well. So it has proved for the Tories. Often the attempts to make themselves nicer and cuddlier worked as perfect “ironic counterpoints” to their sterner policies – a gift to the opposition. No point hugging hoodies while stuffing them in overcrowded jails (during Cameron’s tenure the prison population soared). No point trying to work out how to measure national happiness while austere policies mean some people can’t pay the rent.

Photograph: Gareth Fuller/PA

The focus on foliage and wellbeing that defined Cameron’s early premiership did not age well. After the economic downturn, the Tories soon fled back to their more natural position, as sober custodians of the nation’s finances. In 2013 Cameron was in the centre of a media storm after ordering aides to “get rid of all the green crap” from energy bills as he realised his party risked being seen as high-minded rich people indifferent to the concerns of those on low incomes.

For Theresa May, rebranding to a green and caring image is even less likely to work. First, she has effectively presided over a retox of her party: she has promoted Dominic Raab and welcomed back Liam Fox and David Davis, all of whom have strongly objected to the Tory modernisation project, claiming it takes the party away from its grass roots. Her party’s flagship purpose – Brexit – has anti-modernisation at its very core. Attempting a facelift, at this point, will be painful and difficult.

Second, she is in a far trickier position than Cameron ever was. Cameron recognised his party could not be seen as both “nice” and “effective”, but had to dance between the two. The party could be nice in the good times, as long as it dropped all that to be effective in the bad. It could be nice to attract young voters, as long as it could switch back to being effective when the older and working-class vote fell. May has no such wriggle room.

She cannot afford to lose the support of those on low incomes, and she cannot afford to be seen wasting money at a time when the economy is in peril – her party must project an air of flinty reliability. But neither can she afford to see the Tories abandoned by the young, who are overwhelmingly turning to Labour – her party must be seen to care, too. The task is almost impossible. May, dogged politician though she is, may not be the person to do it.

• Martha Gill is a freelance political journalist and former lobby correspondent. She has worked as a staffer at the Economist and the New Statesman