A woman exits a polling station after casting her vote.

Professor Michael Thrasher, the Sky News boffin, caused consternation on Friday by publishing a projection from the local elections that suggested the results would produce a hung parliament if repeated in the general election. This is where the phrase “just a bit of fun”, a watchword of Peter Snow, the BBC’s former king of the swingometer, comes into play. Thrasher is right to say that if Labour’s share of the vote was seven percentage points ahead of the Conservatives in a general election, the party would probably fall short of a majority in the House of Commons. But that is quite an “if”. That seven-point lead is his estimate of the shares of the vote in the local elections, but other estimates are available. The BBC put Labour nine points ahead. And people vote differently in local and general elections. A lot of people who voted Green on Thursday would vote Labour in the general election. Conversely, quite a few Conservative voters might vote for Reform UK, the rebranded Brexit Party, which didn’t stand many candidates in the local elections.

Nor did Thrasher’s projection include Scotland, where there were no local elections on Thursday, so his figures assumed that Scottish parliamentary seats will stay the same as they were in 2019. Given that Labour is likely to gain about 25 seats from the Scottish National Party, this makes quite a difference, putting Labour on the threshold of a majority. In fact, everything about the local elections — and the Blackpool South by-election — suggests that Labour is heading towards winning the general election with a clear majority. Not as big a majority as Tony Blair won in 1997, perhaps, despite some seat-by-seat projections from opinion polls recently, but a secure majority nonetheless. Yet all this is far too mechanistic. Not only do people vote differently in general elections — and many more people vote in general elections than in local elections — but politics happens. Rishi Sunak has not given up yet, even if many people in his party have. It is true that he has tried to fight back every day since he became prime minister and nothing has worked, but that doesn’t necessarily mean that nothing will work over the next six months.

One thing that the mayoral elections proved, again, is that individual leaders can defy trends. Ben Houchen, the Tory mayor of Tees Valley, has now won three times in an area that should be solid Labour – just as Boris Johnson, his mentor who put him up for a peerage, won twice in Labour London. Sunak has one historical precedent to draw on as he tries to defy expectations in the next few months. When Andrea Jenkyns, the anti-Sunak Tory MP, announced that the coup was off on Friday morning, I was reminded of Gordon Brown in 2009. They said the same about him then that they are saying about Sunak now: that he was leading the party to certain defeat in the coming general election, and that the party’s only chance was to change leader. There was one significant difference between then and now, which is that it was true then that Labour should have ditched Brown – and installed Alan Johnson, the affable working-class Blairite. Labour would have done better in the 2010 election with Johnson in charge. Whereas Tory MPs correctly recognise that replacing Sunak with Penny Mordaunt is not going to improve the party’s chances.

Neither James Purnell in 2009 nor Patricia Hewitt, Geoff Hoon and Harriet Harman in early 2010 succeeded in dislodging Brown. And yet Brown went on to fight the election with such skill, tenacity and seriousness that he clawed back ground from the personable but untested David Cameron and denied the Tories a majority. It is said that focus groups are full of rage against Sunak’s government now, but I remember that Brown was terribly unpopular in the second half of 2009. Not just “he sold the gold”, but a visceral feeling that Labour had been in too long and it was time for a change.