Can the Liberal Democrats and Labour see themselves as allies in a common national project? Or are they fated to behave as rivals, always pursuing different goals? The question has been asked repeatedly, in various guises and circumstances, for more than 100 years, frequently in this newspaper. But there has never been a conclusive answer. Today, as memories of the 2010-2015 Lib Dem-Conservative coalition fade, and following the two parties’ spectacular successes in July’s general election, a new version of the old question is on the agenda. Might the two parties now do to the Conservatives what the Tories and Labour did to the Liberals in the 1920s, and push them to the margins of politics? On the face of it, the two parties are in an unprecedentedly strong position. Under their current leaders, Labour and the Lib Dems share many values, priorities and instincts. Between them, on 4 July, the two parties captured 483 Commons seats: Labour 411, the Lib Dems 72. The Tories emerged with only 121, the worst result in their history. Since July, the Conservatives have shown negligible understanding of why they lost so badly, let alone of how they should face the future. So where might this now be heading? The answer to Britain’s perennial Lib-Lab question always depends on the circumstances. History teaches caution. Merger is not on the cards, nor formal electoral pacts. Coalition, familiar in local government, would be dependent on electoral reform from Westminster. There is no sign of this. But it remains the indispensable and pivotal issue in any serious discussion of interparty cooperation. A new book on a century of Lib-Lab relations by the former Lib Dem minister David Laws reinforces this view. Laws makes the cautionary point that, despite much talking during the past 125 years, there have only been two short periods of genuinely good cooperation – in the 1900s, between Herbert Gladstone and Ramsay MacDonald, and in the 1990s, between Paddy Ashdown and Tony Blair. Could there be a third such phase in the 2020s under Ed Davey and Keir Starmer? Laws displays a greater openness to cooperation with Labour than many might assume given his key role in the Nick Clegg era. But as he told a fringe meeting at the party’s conference last Sunday, the idea of parties working together requires honesty, realism and a forward planning that modern politics rarely allows. Rushing the fences is fatal. Anyone who talks airily about the need for progressive alliances between parties needs to read Laws’ very practical account first. Yet there is an undoubted electoral and political reality for the two parties to work with today. Tactical voting in July redrew the electoral map. There are millions of people – including party activists – who see no difficulty in voting for whichever of the two is better placed to defeat the Conservatives. The parties know this. Too often, however, they refuse to acknowledge it, fearful of offending the tribal cultures in both parties. This coyness was there at this week’s Liberal Democrat conference. It will be the same – probably more so – at Labour’s next week. The consequence is that there is too often a hole in the parties’ messages where honesty and analysis about the way forward should be. The voters are now ahead of the politicians. In his keynote speech on Tuesday, Davey set the Lib Dems an ambitious goal. The Tory party was incapable of providing “responsible opposition” to Labour, he said. “Our job,” he announced, “is to consign the Conservative party to the history books.” This year had been a good start, but now: “Let’s finish the job.” This is a fine and respectable ambition for the third party. But it is hard to take it seriously yet. Even if everything else on the electoral map remains the same – which it will not – it means Davey is setting his party the goal of overturning some very large Tory majorities that easily survived the July rout. Maybe that can be done, but it is a really tough assignment. Listening to Davey’s speech this week, his party may have been lulled into thinking that what they need is one more heave, or that they should return to their constituencies and prepare for another wave of Focus leafletting. But the reality is that any attempt to marginalise the Conservatives, as Davey wants, will have to rely on Labour success too. That’s because the Lib Dems need Labour to maintain its own 2024 wins in the face of renewed challenges from the Tories, Reform UK, the Greens and independents. A swing of 5% against Labour next time would not just upset Davey’s arithmetical hopes of replacing the Tories. It would also mark a change in the political weather, which would make further Lib Dem progress far tougher too. The Lib Dems have an interest in Labour’s success, and vice versa. There were long periods in the past when the two parties’ trajectories were genuinely very different. That’s not really true now. Under Starmer, Labour’s is no longer a socialist project. Under Davey, the Lib Dems have reabsorbed a form of social democracy into their liberalism. For all their faults, both are much closer to one another and to the public mood than the Conservatives now are. The Lib Dems and Labour need to seize the moment. They should use these coming years to promote the kind of nation state and systems of governance they so largely agree on. That means cooperation. It is a joint project, to which electoral reform is the key. If they do not succeed, they will have let down a generation. Martin Kettle is a Guardian columnist