The number of people unemployed in the UK rose by 38,000 to 2.49 million in the three months to June.
This took the jobless rate from 7.7% to 7.9%, the Office for National Statistics said.
The number of people claiming Jobseeker's Allowance also rose, by 37,100 in July to 1.56 million, its biggest increase since May 2009.
The claimant count has now risen for five months in a row to its highest level since February 2010.
The increase in unemployment between April and June came as a surprise to some economists, as most had predicted these figures would show a slight fall in the number of people out of work.
David Kern, chief economist at the British Chambers of Commerce, said the latest data revealed "a worrying rise in unemployment".
"Given the government's programme to reduce the deficit, the figures are not altogether surprising," he added.
"We expect unemployment to increase by 150,000 over the next year or so, peaking at around 2.6 million."
The official figures also showed that between April and June:
- The youth unemployment rate rose to 20.2%, up from 20% in the quarter to March
- There were 949,000 16 to 24-year-olds without work, a rise of 15,000
- The number of unemployed men increased by 18,000 to 1.45 million
- The level of unemployed women rose by 21,000 to 1.05 million - the highest figure since May 1988
- The number of employees working part-time because they could not find a full-time job increased by 83,000 to 1.26 million - the highest figure since comparable records began in 1992
- The unemployment rate remained the highest in the north-east of England, at 10%
- The south-east of England still had the lowest rate of unemployment, with a rate of 5.8%
- The unemployment rate in Scotland was unchanged at 7.7%, in Wales it jumped to 8.4%, and in Northern Ireland it crept up to 7.3%
- Average weekly earnings, including bonuses, were 2.6% higher than a year ago
Chancellor George Osborne admitted the unemployment figures were "disappointing", but said they were not surprising.
"With what is going on in the world economy and with world markets, they are not entirely unexpected," he said.
He added that the government was continuing efforts to help create new jobs, highlighting Wednesday's announcement of 11 new "enterprise zones".
These are designed to boost local economic growth and create more than 30,000 new jobs by 2015.
The chancellor added: "Policies like enterprise zones... are going to make a real difference, I hope, to making sure that those jobs do not just get created in London or the City of London, but actually are generated around the country."
Shadow employment minister, Stephen Timms, told the BBC that the latest unemployment data was "very worrying".
"The economy has flatlined over the last nine months - we're just not seeing the jobs being created that we need," he said.
"Eighteen months after the end of the recession we should not be in a position where the momentum for growth has so clearly run out as it has done.
"And what the government is doing by cutting [public spending] too far and too fast is making matters worse."
Dave Prentis, general secretary of the public service trade union Unison, blamed the increase in unemployment on the government's public sector spending cuts.
"The government's economic strategy is in tatters," he said.
"They need to stop the cuts and restore hope by planning for growth."
Yet, Neil Bentley, CBI deputy director general, said there was some good news in the ONS figures.
"Unemployment rising is a significant concern, but there is some cause for optimism in that over half a million net new jobs were created by the private sector in the last year, and total numbers employed also rose in today's figures," he said.
The latest ONS figures show that between December 2010 and March 2011 an extra 104,000 jobs were created in the private sector, taking the total to 23.08 million.
The number of people in public sector employment declined over the same period by 24,000 to 6.16 million.
Daniel Callaghan, a director at recruitment group MBA, said the latest figures from the Office for National Statistics (ONS) painted a "bleaker picture of the [UK] economy".
"The UK jobs market has been in dire straits over the last few weeks," he said.
"Banking sector recruitment has been frozen and confidence is low in the business market. There is a distinct reluctance among many firms to take on skilled, full-time employees."
The ONS reported last month that the rate of UK economic growth had slowed in the three months to 30 June.
Gross Domestic Product (GDP) grew by 0.2% in the second quarter of the year, down from the 0.5% growth rate recorded between January and March.