Is austerity ending? For some people, in some parts of the country. Philip Hammond used his Budget on 29 October to lavish higher-than-expected tax revenues on the National Health Service, on potholes and on Universal Credit. He also outlined two tax cuts – an increase in the tax-free personal allowance and a rise in the point people start paying the higher 40p rate – which largely benefit the top fifth of earners.

Faced with this, the Labour leadership has a ready answer: while the health budget is rising, across most of the public realm, civil servants and local councillors are still preparing for spending to remain flat in real terms. In other words, austerity is here to stay. It’s a source of optimism to Jeremy Corbyn’s inner circle that Theresa May has moved the economic debate into an area where Labour feels comfortable – arguing about how much extra cash should be put into the public services.

But on taxation, the opposition is less sure of its footing. The party’s official position is unchanged since 23 November 2016, when John McDonnell opted to match Philip Hammond’s pledges on the threshold raise and the 40p rate. That position was repeated in the Labour Party’s 2017 manifesto – yet that seemed to escape the notice of several of the party’s frontbenchers as they attacked the Tories on Budget day. Corbyn described the Conservatives’ tax cuts as ideologically driven, while Emily Thornberry, Angela Rayner and Jon Trickett all condemned the handout on Twitter. That leaves Labour in the odd position, as one frontbencher despaired to me, of “saying that the tax cuts are ideologically driven and poorly targeted – but we’ll keep them”.

McDonnell and his aides are unbowed. They feel they have a good story to tell, pointing out that the “winners” from the 40p rate change include mid-ranking doctors, late-career academics and school leaders, hardly people who can be described as “the rich”. McDonnell in particular is fond of noting that head teachers can scarcely be grouped in with the “1 per cent”, a line to which he returned when briefing the parliamentary press gallery after the Budget. In private, Labour staffers will confess the other reason for supporting the tax cuts: the party’s surge at the last election was helped by former Conservative voters in precisely that £45,000 to £50,000 income band.

We shouldn’t read too much into the difference in tone between McDonnell and his leader, or indeed Trickett (who is one of the “Big Four” attending the Monday afternoon strategy meetings where the party’s direction is decided, alongside the shadow home secretary, Diane Abbott). This is not the beginning of an ideological split over economics.

True, there are issues on which the leadership’s main players are genuinely divided, such as how to tackle the final Brexit vote. At a recent strategy meeting, Andrew Murray – who works part-time as Len McCluskey’s chief of staff and part-time in Corbyn’s office – argued that the Labour Party should vote for Theresa May’s deal to avoid a no-deal exit. At that point, Abbott intervened to disagree. She argued that the party’s pro-European membership would never forgive them for bailing out a weak Tory government and that May’s Brexit agreement would in any case be a disaster that Labour should not be seen to endorse.

Then she warned her old friend Corbyn that their pro-Remain constituents in the north-east of London would be “protesting outside your house” if Labour voted for May’s deal. “That last point really spooked him,” recalls one of the attending staffers.

On tax, however, the divide is the result of tactical missteps and weakness from the leadership rather than a genuine division. Corbyn is not a natural parliamentary performer – he does better out on the campaign trail or in a Question Time-style format – and he prefers to stick to rote lines. He attacked the tax cuts as ideologically driven not because he disagrees with McDonnell’s thinking but because he had geared up to say that austerity was an ideological project regardless of the Budget’s content. Frontbenchers then repeated that message in what was intended as a helpful boost of the leadership. Instead, it left the party in confusion.

Any immediate political fallout is likely to be limited. Yes, McDonnell’s support for tax cuts has been criticised by big names from the party’s recent past (such as Manchester mayor, Andy Burnham) and, more importantly, by backbenchers who are regarded as helpful outsiders by the leadership, such as Lisa Nandy and David Lammy. But Corbyn’s critics have so little credibility with the membership that there is unlikely to be significant pressure to change direction.

The bigger concern for supporters of the Corbyn project is that the split exposes the party leadership’s inability to communicate and explain its policy choices to MPs who need to defend and articulate them. Few disagree that May’s decision to promise the end of austerity was a rhetorical gift to Labour – but even fewer would claim that the opposition has made the most of the opportunity. Although the debate since the election has been on Labour-friendly territory, the party has failed to translate that into increased numbers of voters who say that Labour is better placed to run the economy than the Conservatives.

Privately, Corbyn’s allies have a good story to tell about why that is: they have successfully polarised the electorate and that makes it unlikely that there will be any major shift of support from Tory to Labour, or vice versa, before an election campaign.

That is a persuasive argument for why Yvette Cooper or Stella Creasy wouldn’t be doing better in the polls than Corbyn. It isn’t, however, a compelling argument for why first-past-the-post won’t reward the Tories for merely ending austerity for some people, in some parts of the country.