Welcome to the cherry orchard. In the past 24 hours, the different parties have been picking their fruit from different trees. Rishi Sunak points to Tory gains in Sandwell, Bassetlaw and Stockton. Labour proclaims its triumphs in Swindon, Medway and Stoke. Ed Davey has discovered the national significance of Windsor & Maidenhead. It was ever thus. Thank goodness. Local election results vary because they are, well, local. Nevertheless, national lessons can be learned from the overall results. And however much they differ in public, the parties will this weekend be drawing similar private conclusions – namely that the results are terrible for the Conservatives, just moderately good for Labour and encouraging for the Liberal Democrats and Greens. The prospects of Sunak remaining prime minister after the next election look as bleak as ever. But it remains an open question whether Keir Starmer will enjoy an overall majority in the next parliament or end up leading a minority government, and having to prepare for a second election within a year to 18 months, as Harold Wilson did after Labour’s narrow victories in 1964 and 1974. As for the Lib Dems, their overall vote share is little changed. But they gained ground in a number of their target areas. They must hope that they can repeat their trick from 1997, when the Tories were last ejected from office. Then targeted campaigning and tactical voting enabled the party to double its tally of MPs despite a slight drop in its overall national vote. If they are wise, party number-crunchers will be wary of the nationwide numbers of seats gained and lost. Council election battles come in all shapes and sizes. In Plymouth’s Dunstone ward, John Stephens gained the seat with 2,210 votes. By contrast, in Cotswold district, Ian Watson needed just 336 votes to unseat the Tories and gain Tetbury Town for the Lib Dems. In general, Labour’s gains are tilted more towards large wards in big towns and cities, while the Lib Dems and Greens enjoy most of their greatest success in the smaller wards of less urban areas. This means they are consequently flattered by the figures for their gains. That said, the Conservatives suffered in all kinds of areas, so cannot disguise the scale of their defeat. More useful are the estimates of what the Britain-wide shares for each party would have been, based on the votes cast in areas that held elections. The BBC’s estimate puts Labour on 35%, nine points ahead of the Conservatives, on 26%, and the Lib Dems on 20%. Compared with last year’s equivalent local elections, Labour’s share is unchanged. This must disappoint Starmer. However, the blow is softened by the four-point drop in Tory support. This allows Labour to point to a nine-point lead, its biggest in such elections for more than 20 years. Moreover, that understates Labour’s real lead. In recent years Labour has tended to do worse, and the Lib Dems better, in local than national elections. As a broad-brush estimate, we can add 5-10 points to Labour’s local election lead to obtain a rough sense of the outcome of a snap general election held on Thursday. This puts Labour 14-19 points ahead – which broadly covers the range of recent opinion polls. These figures would give Labour a clear overall majority. How big would depend on how many seats it can gain from the SNP in Scotland, and the extent of tactical voting in England. These local elections confirm the message from recent parliamentary byelections: tactical voting is back. Looking at seats at local level – more useful than their national totals – we see a clear picture of a tactical pincer movement to defeat the Conservatives, with Labour defeating the Tories in some areas and the Lib Dems (and sometimes Greens) in other areas. The numbers are stark. In the first 15 councils that Labour captured, it gained 129 seats, while the Lib Dems gained five and the Conservatives lost 113. In the first seven councils gained by the Lib Dems, the figures were: Lib Dems up 96, Labour up two, Conservatives down 92. All in all, this pattern of gains and losses explains why the Lib Dems are smiling this weekend, even though their national vote share is virtually unchanged. All that should worry the Tories. A similar pincer movement in the coming general election could be fatal to them. But they can point to one potential crumb of comfort. With a general election probably 18 months away, many voters are sending a message rather than making a choice. And abstention can be part of the message. On the BBC, John Curtice said that Labour tended to do better where turnout was down. He made this point to challenge predictions that Labour would suffer from voters needing to present voter IDs at polling stations. But Curtice’s figures could have a completely different explanation: lower turnout helping Labour because disgruntled Tories stayed at home. If they return to the fold at the general election, this will eat away at Labour’s lead. Peter Kellner is a former president of YouGov