For Labour it’s a lack of competence; for the Tories it’s a lack of compassion. Severe, traditional weaknesses which colour each major party in the eyes of the electorate. Sometimes the Labour Party seems like it can’t be trusted with our money and sometimes the Tories look like they don’t care about our problems.

These issues have become, to the frustration of politicians on both sides, a permanent part of each party’s brand – and not without good reason. When Theresa May told the Tories that people thought of them as the “nasty party”, she was on to something. Broad public perception matters more than the individual policies. But individual policies can help to shift the brand.

When the major parties make an announcement, it will always cause more of a splash if it’s a bit counterintuitive – a bit off-brand. Labour announcing tough new spending rules, as John McDonnell did early in his tenure as shadow Chancellor, or the Tories taking an interest in gay marriage or climate change – a big part of David Cameron’s modernisation efforts as a new party leader.

That David Cameron-led detoxification of the Tory Party was the most successful new political strategy this country has seen in the last 20 years. It was led by big, eye-catching changes of direction and it caught the public’s attention.

Today, Theresa May is in need of some of the same magic, and there is a policy area crying out for a bit of surprising Conservative compassion – immigration.

Four developments have made it possible. First, following the Brexit vote, the tabloids have moved on. The number of negative front page stories about the scourge of uncontrolled immigration has fallen through the floor, and relatedly, as Rob Ford has pointed out, so has the salience of immigration and opposition to it.

Second, the Tory benches are stirring. And you can see why – a more sensible approach to immigration appeals to a surprising number of the disparate Tory tribes. For Jacob Rees-Mogg and some of his colleagues at the ERG it’s an issue of ancient freedoms; for the business minded it’s a simple question of economics; for Michael Gove and Boris Johnson, it’s a helpful way to claw back some of their old modernising credentials; and for the Remainer modernisers, like Ruth Davidson, it’s an issue of basic common sense.

Third, we have the Windrush scandal and a new Home Secretary. The disgraceful treatment of the Windrush generation – and the visceral public reaction to it, across all parts of the political spectrum – showed that what matters to the public is fair play. The “hostile environment” had gone far too far and the public, and the tabloids, were rightly appalled. Add to this a new broom at the Home Office in the shape of Sajid Javid, himself the son of migrants, and you can see a clear opportunity to change course.

Finally, the political landscape has changed since the Cameron years. Brexit has killed UKIP, and there is no danger of Labour seeking to outbid the Tories on toughness on immigration. There is now space for the Tories to fill with relatively little to fear in their traditional heartlands.

What’s more, over the long term the Tories cannot afford to be left with an ever-decreasing base. As Global Future analysis shows, the rotation of the political axis from the old left/right division to Open vs Closed is reshaping our politics.

For the Conservatives the temptation to identify even more strongly with Closed, thus hoovering up the remnants of Ukip and building a bridge to Labour Leavers, is obvious. However, ultimately this means chasing an ever-shrinking coalition and entrenching deepening the age divide that cost them a majority in 2017. At the risk of putting too fine a point on it, the Open side is growing, whilst the Closed side is dying off.

So what’s stopping them? Unfortunately her name is Theresa May, and she is the Prime Minister. But when the conditions change good politicians change their minds. U-turns are one of the most misunderstood actions in politics. As long as a government doesn’t earn a reputation for constantly changing its mind, a u-turn is a sign of intelligence and strength. A move that says I have listened, understood and been big enough to admit that things can improve.

This government’s immigration strategy can surely improve. The tens of thousands target is a soundbite that drives dreadful policy. The hostile environment, the bizarre attempts to hamstring our world-leading universities and the ludicrous refusal to allow visas for the doctors our NHS needs, are all driven by a policy that was plucked out of the air. And that’s aside from the fact that our aging population and faltering economy need more migrants every year to keep our country going.

The government are working on an immigration white paper as we speak. Theresa May could revitalise her premiership by making a big, bold step in the right direction. Drop the target, drop the hostile environment and come up with something sensible that will help facilitate the Global Britain her government is committed to creating.

The question isn’t why make the change – on policy and on politics the case is growing stronger by the day. The question is why not?