Britain’s labour market is cooling, with annual earnings growth easing markedly and the number of job vacancies falling for a 25th month in a row.

Or is it? The number of people in work climbed by almost 100,000 in the three months to June while the jobless rate fell from 4.4% to 4.2%.

The picture is confusing, to say the least, but look closely at the latest bulletin from the Office for National Statistics and some themes stand out.

Related: Jobs market uncertainty causes headache for Bank of England rate setters

One is that there is no evidence of a wage-price spiral. Annual growth in total earnings – regular pay plus bonuses – was 4.3% in the three months to June. That is down from 5.7% in the three months to May and half the 8.6% recorded in June 2023.

Part of that decrease was due to last year’s high NHS bonus payments not being repeated, but there was still a fall in annual earnings growth – from 5.8% to 5.4% – once the impact of bonuses is stripped out. Pay deals seem to be responding to the fall in inflation back to the Bank of England’s official 2% target in May and June.

A second theme is that employers are starting to hire again as the economy emerges from its soft patch in the second half of last year. Trends in unemployment tend to lag behind what is happening to economic activity – but the recession of late 2023 was short-lived and growth has bounced back.

Despite what Rachel Reeves might say about being the chancellor with the worst inheritance since the second world war, the labour market figures suggest Jeremy Hunt bequeathed an economy that was on the mend and – by recent standards – in reasonable shape. Unemployment is down and employment is up. That said, firms are still showing a degree of caution. The number of part-time workers rose by 144,000 in the three months to June, while the number of full-time workers fell by 48,000.

Thirdly, while the overall picture looks relatively benign, deep structural problems remain. More than 2.8 million people are economically inactive because of long-term ill-health, while the labour market has become more dependent on workers born outside the UK. The number of UK-born workers in employment has fallen by 316,000 in the past year, while the number born in other countries has risen by 249,000.

The curate’s egg nature of the latest ONS figures – good in parts – means they are not much help for the Bank’s interest-rate setters as they contemplate what to do with borrowing costs. They do, however, highlight some important issues that government ministers – Reeves, and the work and pensions secretary, Liz Kendall, in particular – need to address.