The queues for the “Birmingham tapestry” on the opening day of the Tory conference is a merry spectacle for a leadership often accused of lacking attention-grabbing ideas. A tableau of a miserable Keir Starmer greeted by unimpressed peasants gives way to the Burnham era and taxpayers facing an arrow to the eye as “Healey’s comet” heralds tax rises for the middle class. Reform apostates cower under the stern glare of a Kemi Badenoch and “Farage fighteth with a bin” jokes. 1066 is a fertile field for something today’s Tories have lacked: a sense of confidence in their own story.

One thing Badenoch does not lack is self belief. Her opening speech channelled the spirt of Margaret Thatcher – always a dangerously high bar for Tory leaders to emulate – declaring: “We governed for 18 years because we started with the right foundations.” The economy and how to pay for defence spending are the dividing lines she is keenest to draw with Labour this week. We started as no doubt we will go on – with Kemi-style scolding about Britain has become “very complacent” in recent decades and taken growth for granted.

Showing that the Conservatives have their moxie back is a key aim of this conference. Badenoch has had a far better year than the one leading to 2025’s anxiety-ridden Tory clan gathering. Her personal ratings are markedly improved, and more people are willing to at least give the party a hearing. Yet only a fifth of people believe Conservatives are ready for a return to government – three-fifths think they are not (and the rest haven’t given the matter any thought, frankly).

To exorcise the ghosts of past failures and move her own story along the tableaux of national life, Badenoch needs to look like she has more than a Bayeux-style critique of enemies to the left and the Reform-focused right. She needs an offer which reaches beyond the pensioner vote, still the most loyal group of her voters, and which also creates a pain point for a reinvigorated Labour party.

To that extent, the “Burnham bounce” also offers opportunity. As the Labour leader leans more explicitly into the need to use tax-rises and its overhaul of the triple lock to pay for its social care reform, Badenoch will argue that when you scale focus back from grand future schemes like the social care plan (whose precise costings and delivery remain elusive) raising the question of EU membership, and which electoral reform Labour wants, the Government is by-passing the more immediate concerns of many middle-class voters.

Much of the past year has been spent behind the scenes figuring out where the Tories should place their chips to win back voters. The former shadow chancellor Mel Stride was keen to have an offer for younger people desperate to get on the property ladder. That focus has shifted as Badenoch announces what aides want to frame a “bazooka” proposal: the pledge to remove the £100,000 threshold for tax-free childcare and free childcare hours, agreed under the Cameron government.

It is unashamedly targeted at more prosperous families, which means that Labour and other critics can roll out the “tax breaks for millionaires” argument (based on the fact that these earners will likely have property in the million-plus bracket). “Crazy – a gift to us,” texts one Labour advisor. But is it?

This move opens up an area of competition on economic efficiency the Tories want to engage directly with, namely, policies which unintentionally create a lack of incentives for people to work. In the case of higher earners hitting the £100,000-club – which has risen to over 2 million people this year – they are worse off overall even if they take on extra work or are rewarded by a hefty pay rises.

Inflation and house-price rises have made this threshold a lot less generous that it was over a decade ago. Those earning just over £100,000 and under £125,000 end up with a marginal tax rate of 60 per cent, while childcare support can cost around £20,000.

The freezing of tax allowance thresholds will also pull more earners into this zone by the end of the decade. Badenoch also knows that for many voters, this will seem like an odd use of (theoretical) largesse. But it is about muscling her way into a conversation on what sort of moves we need to rev up the spluttering engine of the national economy.

Labour will argue that any advantages in allowances and offsets need to be focused lower down the earnings curve. But there is also a challenge here for John Healey, sweating in a fiscal corset as he pens the upcoming Budget. If the Tories are planning on showing their colours as supporting families who feel that they are doing well – the HENRYs (High Earners Not Yet Rich) – what offer does a government which is taking its time reducing the welfare bill have for the better-off?

The winners of a sclerotic tax system are not really the low end of the “millionaires”, but the ultra-wealthy, who have assets which escape the ordinary tax net and benefit from reasonable Capital Gains taxes. (It would be interesting to hear what Badenoch has to say about that.)

The political thrust this week, however, is that it does indeed draw a clear blue line with Labour – but it does so on a territory where she wants to fight her corner. The Conservatives will be less squeamish about the need for dynamic incentives to earn well and to retain more of the most productive people in full employment. The UK’s productivity gaps with competitors are still wide – and the Government’s growth recipe is tied to the less certain returns of devolution.

At the same time, Reform’s tax and economy plans are wildly free-wheeling, and its friendliness to cryptocurrency and wealthy donors take Nigel Farage’s party into territory which feels distant from even the “ordinary” prosperous voter.

Crucially, the political battlefield for Badenoch is to find reasons why “soft” Reform voters should return to the Tory fold too, and offer a policy which is clearly Conservative in its gut belief in people being better rewarded for their successes – but not bogged down in competing with Farage and her old frenemy Robert Jenrick.

It is also asking questions about the impacts of tax systems which the other parties have skirted – which is why more people who are well off, but not super-rich, are paying a lion’s share when they are raising families. It’s not an argument to impress a consensus basking in the afterglow of Burnham’s speech – because it’s not really a proposal for them. It’s a move from Tory leader who wants to sally onto the battlefield of taxation where she believes the government’s vulnerabilities will ultimately lie. Arrows will duly fly.