Britain's nascent economic recovery is yet to be felt in workers' pockets, with wages rising at a paltry 0.7% in the year to August while prices grow almost four times faster.

Unemployment declined by 18,000 in the three months to August, to 2.49 million, according to the latest official snapshot of the labour market, and the number of people in work hit a fresh record high of 29.87 million people.

However, the strengthening in the labour market has not yet been reflected in the kind of pick-up in wage growth economists have been hoping for to translate the early signs of recovery into a solid upturn.

The Office for National Statistics said total pay rose at an annual rate of just 0.7% between June and August. Excluding bonuses, pay growth was marginally stronger, at just 0.8% – the weakest figure since comparable records began in 2001. Inflation was running at 2.7% in August.

These latest figures will help to underpin Labour's claims that while the economy may have "turned a corner" as the chancellor suggests, many ordinary families are still suffering a "cost-of-living crisis".

James Plunkett, of the thinktank the Resolution Foundation, said: "It is now well-established that this has been a tough downturn for wages. The fall in real wages we've seen has been unprecedented. But perhaps most worrying today is that there's still no sign of the wage squeeze ending – despite some better economic news, the gap between pay and prices is wider now than it was a year ago."

Pay is particularly weak in the public sector, the details of the ONS data reveal, declining by 1.6% in the year to August. Much of the fall came in the state-backed banks, where bonuses were down, and the make-up of the workforce has shifted towards lower-paid staff.

But even excluding financial services, public sector workers saw their pay decrease by 0.8% in the year to August: the weakest since records began in 2001, against a background of above-target inflation.

John Philpott, of the consultancy the Jobs Economist, said: "Workers in the public sector are now bearing the brunt of the real pay squeeze, adding to the pain imposed by job cuts in the order of 10,000 per month. This degree of real wage squeeze is not conducive to a strong and sustained recovery in the UK economy."

The unemployment rate – closely tracked by the Bank of England, which has promised not to raise interest rates until it falls at least to 7%, provided inflation remains under control – was unchanged, at 7.7% between June and August.

On the more timely claimant count measure, which only takes into account people receiving out-of-work benefits, unemployment fell by a chunky 41,700 between August and September, to hit 1.35 million. Meanwhile, the number of vacancies available across the economy hit its highest level since 2008, the ONS said.

Young people appear to have been left on the sidelines as the jobs market has recovered over the past 12 months, however, with unemployment among 16- to 24-year-olds almost unchanged at 958,000 between June and August.

Despite the unchanged unemployment rate, City analysts said the strong improvement in employment suggested the Bank might have to tighten monetary policy earlier than 2016, when it expects the unemployment rate to have hit its 7% threshold.

Howard Archer, of consultancy IHS Global Insight, said: "Although the unemployment rate was stable at 7.7% in the three months to August, the healthy overall tone of the labour market data does little to dilute expectations that it will get down to 7% well before the Bank of England is currently forecasting."

Chris Williamson, chief economist at Markit, said: "The upturn is welcome news as far as the economy is concerned, but raises the possibility that the Bank of England has underestimated the speed with which the economy is reviving."