If traditional assumptions still mean anything at all in British politics, the Conservatives were there for the taking in this week’s English local elections. In power at Westminster for eight years, the economy stalling, Brexit going badly, the cabinet split, ministers resigning, council taxes rising and the Windrush scandal still vivid in the public mind, Theresa May’s party was a sitting target for an opposition party with hopes of general election success. In the past, Labour might have swept the Tories out of town halls across the country, with the Liberal Democrats pocketing plenty of gains too.

This didn’t happen on Thursday. That is a significant event in itself. The post-election analysis, particularly in the Labour party, requires humility, not least because Labour had talked up its chances, especially in London. But the inquest will need open-mindedness as well as humility. Labour did not capture the London boroughs it dreamed of, and it did badly or not well enough in many places outside London. Nevertheless, Labour ran neck and neck with the Tories – 35% to 35% – in the projected national share of the vote (last year the Tories had an 11-point lead), won its best share of the local election vote since 2012 and, in London at least, it turned in some of its best borough performances for a generation.

One way of reading this week’s results is to say that nothing much happened on the broad canvas, so that Thursday was overall a vote for the status quo and respective comfort zones. Relatively few local councils changed hands. No major party harvested massive seat gains. Everyone had some losses as well as wins. The two main parties were head-to-head in the opinion polls beforehand and still head-to-head when the votes were counted. Separate general election projections by the BBC and Sky News show both Labour and the Tories well short of an overall majority on the basis of this week’s voting . The one major caveat to this no-change reading is the collapse of Ukip, which was all but wiped out in these contests. Good riddance, and to the smaller hard-right parties too. Ukip and leave voters gravitated heavily to the Tories this time, a very mixed blessing for Mrs May in her Brexit battles.

The Conservatives undoubtedly managed public expectations about these elections better than Labour. Party chiefs had talked their chances down to floor level before Thursday. As a result, the Tories’ narrow retention of fortress London boroughs like Wandsworth and Westminster – and the capture of Basildon and Peterborough – could be spun into a successful night’s work. In fact, the Tories had a three-point drop in share of the vote, a small net loss of councillors and were ousted in their flagship northern council Trafford. Yet Mrs May’s bruised and battered leadership, which many thought would become an issue if the results were bad, has survived yet again.

Both the Greens and, in particular, the Liberal Democrats had decent nights. The latter did well in south-west London, won the mayoral contest in three-way Watford, regained Three Rivers and South Cambridgeshire and registered gains in many parts of England, from Cheltenham to Hull. But this is hardly a revival, more some decent bits of rebuilding. Even with Thursday’s 16% national share, the Lib Dems would be hard put to hold the balance of power at Westminster, according to BBC projections.

The biggest questions from these elections are nevertheless those for Labour. Jeremy Corbyn always depicts a Labour party itching for a general election and confident it can win. These results do not rule that out. But they do suggest that there are difficult hurdles still to overcome. Labour’s vote share dropped from the general election. It did well in London and other cities; but it lost ground in many towns, north and south. It was taken to the second count before winning the mayoral vote in the Sheffield city region. Its position in Scotland, where there were no elections, remains difficult. The antisemitism row harmed the party in areas with significant Jewish votes. That issue, along with ambivalence about Brexit, leaked some support to the Lib Dems and the Greens. It is dishonest to say Labour had a disastrous night on Thursday. But it was certainly not a triumph either – and that could be the more lasting lesson.

• This article was amended to clarify that the mayoral election in Sheffield was for the city region, not the city.

