Rishi Sunak may see himself as a future prime minister but this budget confirmed he is very much Boris Johnson’s chancellor.

Rumours about ructions between the pair have gripped Westminster for months. Sunak, who told last year’s Tory conference his party had a moral duty to fix the public finances, was known to be queasy about the government’s national insurance increase, for example.

But ultimately Sunak was left with little choice. Johnson has long been sceptical about the idea of austerity and is keen to have something to show so-called red wall voters in exchange for their support in the 2019 general election.

Fortuitously for both men, the independent Office for Budget Responsibility (OBR) significantly upgraded its forecasts for the public finances, handing Sunak a helpful windfall, much of which he has chosen to spend almost immediately – £25bn in 2022-23 alone. So there was extra cash for schools, “family hubs”, transport infrastructure and a string of other causes.

But Sunak switched to a completely different register when he delivered the one passage of the budget in which he seemed truly himself – a tribute to Thatcher and cutting taxes, at the end of his hour-long address to parliament.

Despite propelling the tax burden to its highest peacetime level – through a combination of next April’s national insurance contributions (NICs) increase and a sharp rise in corporation tax due to take effect in 2023 – the chancellor painted himself as the champion of low taxes.

More than that, he signalled he intended to cut taxes on “work” by the end of this parliament – an odd claim for someone who has just implemented a NICs rise.

“There’s a reason we talk about the importance of family, community and personal responsibility. Not because these are an alternative to the market or the state … it’s because they are more important than the market or the state,” he said.

“As we look towards the future, I want to say this simple thing to the house and the British people: my goal is to reduce taxes. By the end of this parliament, I want taxes to be going down not up. I want this to be a society that rewards energy, ingenuity and inventiveness. A society that rewards work. That is what we believe on this side of the house. That is my mission.”

This section of his speech was greeted with enthusiasm on the Conservative benches behind him.

Despite welcoming a new bypass, hospital upgrade or museum refurb to put on the next election leaflet, many Tory MPs have niggling worries about where Johnson’s cakeist instincts when it comes to public spending are taking their party.

The Sunday Times reported just before the Tory conference in Manchester last month that Johnson and Sunak had struck a deal: the chancellor would sign off on some of the prime minister’s spending priorities as long as he could maintain enough fiscal headroom to deliver tax cuts before the next general election.

The reports were played down by both sides at the time but Wednesday’s statement neatly fitted that narrative. Sunak dressed up the larger-than-expected cut in the taper for universal credit as a downpayment on his tax-cutting pledge – though it could perhaps more accurately be described as a partial U-turn on the widely criticised cut he insisted on.

Meanwhile, it felt in the Commons on Wednesday as though Johnson was very much in the ascendancy. While he talked of an “age of optimism”, Sunak cannot carry off boosterism as convincingly as his boss.

And the OBR’s forecasts told a very different story to the budget rhetoric when it came to the everyday lives of voters. Real disposable incomes are expected to take another three years to return to pre-pandemic levels, despite the prime minister’s promise of a “high-wage economy”.

With a tough winter ahead, both Sunak and Johnson may have left themselves exposed to the public’s sense that real life fails to match the sunny picture they have painted. And it remains to be seen whether Sunak’s pre-election tax cut gameplan works out – what the OBR gives, it can take away.

But for the time being, it feels as though Johnsonism – with its infrastructure spending and red wall handouts – is winning out over whatever Sunakism might turn out to be.