A faraway scene comes to mind when I think about the Conservatives and black Britain – and it should trouble Theresa May as she surveys the wreckage of the Windrush fiasco. It is of a man who lives in my father’s Jamaican village, at the top of the hill, who each day has to come down to the village square to fill plastic barrels with standpipe water. Once I tried to help him carry just one of them and almost suffered a hernia. He is the epitome of what brought the Windrushers to Britain. The social services are minimal; the communal provision is patchy. They are people who know that, by and large, what they need they must eke out for themselves.

Margaret Thatcher, had she not been gripped by irrational dread of “alien cultures”, would have liked their way of thinking. Certainly her party as we know it today should benefit from a younger generation whose political thinking has been inspired by can-do forebears, especially as they move into higher income and social demographic groups.

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The reason it does not is that, through words and deeds, the Conservative party presents to a critical mass of black people as racist. Think of the Commonwealth Immigrants Act 1962, custom-built to restrict black migration and condemned by Hugh Gaitskell as “cruel and brutal anti-colour legislation”. Think of the 1964 Smethwick election, with its unofficial Tory candidate slogan: “If you want a nigger for a neighbour, vote Labour.” Think Enoch Powell. Think Thatcher’s Powellesque warnings about the country being “swamped by people with a different culture”.

Give David Cameron his due. He may now be reasonably depicted as the most disastrous prime minister since Anthony Eden, but at least he understood how damaging it was that his party had made itself repellent to growing sections of the electorate. Goaded by research from former deputy party chairman Lord Ashcroft that showed the depth of minority antipathy to the Tories, he sought to rewrite the narrative – and did so, with some success.

In 2015 the Conservatives received 33% of black and ethnic minority votes (1 million). This was less than Labour – who captured 52% – but way up from 2010, when the Tories got just 16% of the BAME vote. This is the progress that May has trashed with her pandering to Brexiter rednecks, with her pathological, longstanding obsession with immigration, and her acceptance of – perhaps connivance with – the unthinking bureaucracy that led inevitably to the Windrush scandal.

Profile How the Guardian broke the Windrush story Show Hide In November last year, Paulette Wilson (left), who has lived in the UK for more than half a century, spoke to the Guardian's Amelia Gentleman about her treatment at the hands of the Home Office - and revealed that she had been held at Yarl’s Wood detention centre and threatened with deportation. It was the first of a series of stories that developed a picture of how many members of the Windrush generation were being mistreated by the government under the so-called ‘hostile environment’ policy. By February, with other examples mounting, the government had relented in Wilson’s case, but faced acute criticism from Caribbean diplomats who urged the Home Office to adopt a “more compassionate” approach. In March the story of Albert Thompson - who had lived in Britain for 44 years but was told to produce a passport or face a bill of £54,000 for cancer treatment - forced attention back to the growing crisis. After the Guardian reported a string of additional cases matters came to a head when Theresa May refused to meet with Caribbean diplomats to discuss the issue, prompted fury among opposition MPs and a wider media backlash. After days of negative publicity, the then home secretary, Amber Rudd, and May were forced to change tack and issued apologies, promised reforms – and eventually gave the Windrush generation a fast-track to citizenship. Photograph: Fabio De Paola

And so we encounter a familiar sight: that of the prime minister and her lieutenants, shovel in hand, frantically digging themselves out of a hole. If you bow at all, bow low, says the Chinese proverb. On Monday the home secretary, Amber Rudd, followed that advice to its extremes. Guaranteed citizenship for any of the mistreated Windrush generation, compensation for their often “heartbreaking” treatment, fees waived, no requirement for applicants to take the obligatory knowledge test on language and life in the UK. A new customer support centre. After months of disdain and indifference to their plight, goodwill abounds.

And suddenly the new mood, this government’s cultural glasnost, reaches into other areas. While Rudd bows low, May, fresh from the memorial service marking 25 years since the death of Stephen Lawrence, unveils an annual national day of commemoration for him. Within days, we have lurched from famine to feast.

It doesn’t pay to be too cynical. The Windrushers deserve to be fairly treated. The Guardian, through the reporting of Amelia Gentleman, has been seeking that outcome for months. Of course Stephen Lawrence deserves a day. The commemoration of what the Lawrences and their supporters did for equality and social justice in Britain deserves a slew of days.

But what we see is not a government responsive to the public mood, agile in thought, decisive in action, sound in judgment. It’s a study in rush and chaos. There is no method. Its rallying cry is the alarm behind the broken glass. It resists, and when resistance becomes futile, it reacts. Neither position seems the result of much thought. There is no programme, no coherent philosophy, just responses to chatter and evasive action to fend off the impending calamity of the hour, whether by belatedly addressing it or by doing something else to divert attention.

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Plastic bags, Grenfell, modern slavery, social disparity, housing shortages, apprenticeships: the list of issues the May government has flapped at in a now characteristic half-hearted way grows daily. She promises to tackle racial inequalities. She makes a totem of it. Next stop, Windrush scandal. Her government cannot buckle down and govern in any measured, coherent sense. It is giddy, confused, arrogant, afraid; terrified of threats from a resurgent Labour without and careerist mutineers within – and buffeted throughout its flight by the wild turbulence of Brexit. How can it do anything other than stagger the length of the aircraft applying sticking plasters?

Even a prime minister with the appropriate skillset of vision, efficiency and empathy would struggle. Theresa May, lacking all three, doesn’t stand a chance. The result is what we have witnessed. Her government, until it was shamed by the media and the public, did not have the wit or ability to address the Windrush issue until it raged around them – even though it had half a year to see it coming. That should worry us. And that failure has widened a chasm between the Tories and the voters they need and should be able to engage with, many of whom now live in Conservative suburban marginals. That really should worry them.

• Hugh Muir is associate editor of Guardian Opinion