Labour can win a majority at the next general election. Thanks to a much better-than-expected campaign for Jeremy Corbyn and a disastrous one for Theresa May, the party made significant progress towards power on 8 June.

If the old adage that “oppositions don’t win elections, governments lose them” is anything to go by, Labour is well-placed to make further gains: the tremendous challenges the government faces in negotiating Brexit, dealing with its consequences, and passing bills in parliament without a majority, mean Labour could well go into the next campaign as the favourite.

Yet while it would be silly to try to make any predictions about the next election, there are good reasons to think Labour will face a much tougher challenge achieving the 64 gains it needs for a majority, than the 30 made earlier this month.

Labour’s plans will undoubtedly face greater scrutiny next time around, and there was certainly a group of Corbynsceptic voters this time that felt they had a “free pass” to vote Labour, confident that Corbyn would not become prime minister. The key unknown is how big that group was, and whether they have come around to Corbyn since the campaign.

The broader issue, though, is Labour’s continued difficulty with lower-middle class voters. Despite huge swings to Labour in boho places such as Hove and Bristol West, Labour actually went backwards in a number of what are now its target seats: Stoke-on-Trent South, Bolton West, Mansfield, Copeland, Morley and Outwood, and Corby.

As Policy Network’s new analysis shows, Labour had a particular problem among voters with household incomes of between £21,000 and £34,000, and typically in the C2 social grade. The seats Labour needs to win have a disproportionate number of these voters, compared to the ABs with whom it performed so well. Labour’s electoral coalition increasingly resembles that of the US Democrats, composed to a considerable degree of the young, the well-educated, ethnic minority voters and those on the lowest incomes.

This is not to say Labour couldn’t make further gains with a “one more heave” approach at the next election. There are even more young voters to excite and turn out (what we might call the “Bernie Sanders” strategy), and every year that passes there will be more graduates and Britain will be more ethnically diverse than before (although it is also getting older). While recognising the immense difficulties in doing so, there are, however, two reasons why I would prefer Labour to try to build a broader coalition than this.

The first is short-term. With the “Bernie Sanders” approach, Labour might be able to make enough gains to cobble together a relatively weak, minority government as Theresa May has just about managed. But we can see the problems with this – the government has been forced to significantly water down its proposals, and already looks as though it is on life support. Governments – all governments – have to take tough decisions, and are held accountable when they do so. To achieve big legislative changes, they need the leeway that a working majority provides.

To win a majority of one, or better, a majority of 50 that could serve as a platform for a transformative two or three-term government, Labour needs to build a cross-class coalition as broad as the one Clement Attlee achieved in 1945. It means building support across the whole country, encouraging all voters to get behind a project using the rhetoric of “collective national renewal”, not appealing to sectional interests. Microtargeting has a role in any campaign, but the tone and policy offer should be broad enough to appeal to “communitarian” as well as “cosmopolitan” Britain.

The second reason is long-term. Even if Labour could win a large majority just by attracting even more young professionals and graduates, in the long-term this could cause real damage to the health of our democracy. Labour was founded as the party of, and by – as well as for – working-class people. Throughout its history it has been closely bound to the institutions of collective self-help: trade unions, co-operatives and mutual societies.

Doing good things for the people, but not involving them or promoting a sense of joint ownership in the process, is insufficient. All the issues that were raised in the aftermath of the EU referendum still apply: communities felt ignored by politicians, leading many to give up voting, while others were increasingly willing to register protest votes on issues where they felt they had not been listened to. While the Conservatives have attempted to tap into these concerns, it is Labour that has a specific civic duty – as a result of its history and founding purpose – to bring these people back into the fold, to bridge the divide.

Read more: History suggests an early election. Economics points the other way

How Labour achieves that is still very much an open question. Despite the surprise election result, the new fundamentals of British politics – the cultural dividing lines that have emerged in recent months and years – have not gone anywhere.

Charlie Cadywould is a researcher at Policy Network, and co-author of a report on Labour's future, The Broad Church.