Public sector job cuts imposed as part of the government's austerity drive have sent unemployment back through the 2.5m barrier, according to official figures released on Wednesday.

The Office for National Statistics said the number of people out of work rose by 80,000 in the three months to July, reaching 2.51m, mainly due to a sharp rise in youth unemployment.

Despite ministerial hopes that the private sector will be able to compensate for the squeeze on the public sector, the ONS said the May to July period had seen the sharpest rise in unemployment in two years.

The unemployment rate using the internationally agreed yardstick for calculating joblessness rose to 7.9% for May to July, from 7.7% in February to April.

Officials said that employment in the public sector had fallen by 111,000 in the second quarter of 2011, the biggest drop since recent records began in 1999.

The government's alternative measure for unemployment – the claimant count – indicated that an additional 20,300 people were out of work and claiming benefits in August, a smaller increase than the City had feared following an increase of more than 30,000 in July. The claimant count total now stands at 1,580,900.

Unemployment on both measures has been rising in recent months as the UK's recovery from the deep recession of 2008-09 has stalled. Economic output has increased by just 0.2% in the nine months to June.

The ONS data showed that employment in the three months to July fell by 69,000, the weakest performance since spring 2010. Employment minister Chris Grayling, said: "Today's figures underline the scale of the challenge that we face particularly given slower growth across Europe and North America. Unemployment remains lower than it was six months ago but clearly we must continue to focus our efforts on supporting business growth and ensure that people who do lose their jobs have the best possible support to get back into employment."

Youth bear the brunt

Unemployment among 16-24-year-olds, the age group worst affected by the slowdown in the labour market, rose to 972,000 in the three months to July as school leavers and graduates struggled to find work. Among those aged between 18 and 24, the unemployment rate now stands at just under 19%, more than double the jobless rate for the UK as a whole.

TUC general secretary Brendan Barber said: "These are terrible figures. They are further evidence that the recovery has been choked off by a self-defeating rush to austerity. Government policies are hurting, but they aren't working.

"Most worrying are the signs of a second wave of rising young unemployment – with the number of 18-24-year-olds out of work now higher than at any point during the recession – making the government's decision to slash the support to young people through Educational Maintenance Allowances and the Future Jobs Fund look even more short-sighted and cruel," Barber added.

A breakdown of the ONS data showed that public sector employment was 3.8% lower in the May-July period of 2011 than it was a year earlier, while private sector job growth has slowed – up 0.2% on the quarter and 1.2% on the year.

The number of people working part time because they could not find a full-time job reached a new record level.

Michael Saunders, economist at Citi, said: "Worse news probably lies ahead. The number of redundancies is up 40% quarter on quarter, while vacancies are falling. Private sector employment is likely to weaken further as firms cut back on labour use, and firms may well cut back rather more quickly than in the early stages of the recession because there currently is less offsetting stimulus from new falls in interest rates. The jobless total is likely to rise above the recession peak soon, and probably will reach 2.7-2.8 million people (8.5%-9% of the workforce) during next year."