For some, any idea that Keir Starmer and audacity are words that can sit comfortably in the same sentence will seem nonsensical. To many who define themselves as Labour supporters, the most salient characteristic of the opposition leader is not his audacity but its opposite, timidity. In this critique, Starmer’s strategy, if he really has one, is to do as little as possible to offend the voters, and wait for the Conservatives to eject themselves from government by their own divisions and incompetence rather than to drive them from it. Seen thus, the English local elections of 2023 were quickly interpreted as an object warning on the limits of this supposed approach. The Conservative vote share on 4 May was predictably down after the negligence and bloodletting of 2022. Labour’s lead, though, was more modest, so the spoils were shared with the Liberal Democrats and Greens. After the voting, a Labour landslide no longer beckoned as brightly. Instead, the future seems more likely to offer a hung parliament and talk of coalition deals. This scenario certainly cannot be ruled out. But it is absolutely not Starmer’s own strategy, which is for Labour to win outright. Starmer’s advisers do not believe the local elections were disappointing. They think they are very much on course, and have read the results much more positively than the Starmer sceptics. This partly explains why the party hierarchy was so agitated about the media’s instant focus on hung parliaments and coalition possibilities. At the core of this more favourable reading to Starmer is the fact that Labour did noticeably better this month in areas that voted leave in the 2016 Brexit referendum, many of which (the so-called red wall) Labour lost to the Tories in 2019. By comparison, this month’s results were less striking in areas that voted remain, where the Labour (and Lib Dem) vote was already fairly strong. The inferences are twofold: that Labour is now doing best where it matters most, and that Brexit is no longer defining the electoral map. For example, there was a seven-point swing to Labour a fortnight ago in areas won by the Tories in 2019. This compares with a swing of just under three points in areas won by Labour in the same year. Another finding in a similar vein is that Labour also did best this month in areas of England with fewest university graduates where it netted a six-point swing. In places with more graduates, the swing was only three points. If it is sustained, this disproportionate shift to Labour among working-class voters has the potential to be significant in two ways. The first, and more immediate, is that it puts more Conservative seats within reach for Labour. The second, with even longer-term implications for electoral geography, is that it points towards Labour reuniting its working-class and middle-class tribes after the fissures caused by Brexit and Jeremy Corbyn. Each of these is a central strategic aim for Starmer, and each needs to be properly understood. Starmer’s course has been consistently set towards winning an outright Commons majority in 2024. When he was elected leader, he never settled for the two-term recovery many assumed he would need after the hammering Labour received at the 2019 election. Equally important is that the progressive prospectus he intends to offer is a national one, based on reunifying the class base of the Labour electorate rather than accepting its irresistible divergence into a delta of different political parties and traditions. To state these things is neither to endorse the approach nor to dismiss it. But it is to emphasise that this is indeed Starmer’s aim, and that it is remarkably bold. It flies in the face of a considerable amount of conventional wisdom about 21st-century British electoral behaviour. To aim at winning an overall majority in one term, after Labour was reduced to its lowest seats total since 1935, is itself audacious. To seek to do it on the basis that Labour can again be a national party in geographical and class terms, winning working- and middle class support alike, deserves that description even more. Starmer’s view puts him at odds with one of the most widespread assumptions on the European centre-left. It challenges the view that the dominant progressive parties of the industrial era must accommodate themselves to operating within a more pluralist party system and amid the looser class loyalties of the new millennium. Instead, it says that such segmentation is neither inevitable nor even desirable, providing that the party remains a broad church and – crucially – avoids foolish accommodations with the activist left. But it is certainly not New Labour 2.0 either, and calling it so does not make it so. Indeed the Starmer strategy of focusing on working-class support is at odds with one of New Labour’s most central tenets. Tony Blair and Gordon Brown believed that Labour would prosper in the modern era only by reducing its dependence on working-class voters and the unions and by becoming a middle-class, progressive party, like the US Democrats. Starmer, by contrast, is very deliberately trying to turn towards working-class voters, not away from them, and to engage with and speak for their concerns. It is one of the reasons he focused on housebuilding on Wednesday. This is actually quite a traditional, and almost old-fashioned, view of Labour’s role. Starmer’s aspiration to make Labour a national and essentially social democratic party again is one that Clement Attlee or Harold Wilson would have understood. In the vastly changed economic and political circumstances of the 2020s, it is hard to find a more appropriate word than audacious for this attempt to reforge the sword that was broken. The key, obviously enough, is whether it succeeds. Martin Kettle is a Guardian columnist