The Office for National Statistics (ONS) said the UK unemployment level fell to 2.46 million after the biggest quarterly decrease for three years.
The drop came after a 184,000 increase in the number of employed to 29 million, marking the largest quarterly hike since the three months to May 1989.
Employment rose as the number of part-time workers lifted by 115,000 in the quarter to a record 7.84 million - suggesting more people are struggling to find full-time permanent jobs.
But the ONS said there was also a lift in those in full-time work, up by an encouraging 68,000 to 21.2 million in the quarter to June.
Today's figures also show the sixth successive fall in the claimant count for those on Jobseeker's Allowance, down 3,800 to 1.46 million - although this was far lower than expected by analysts.
And the ONS revised down last month's quarterly fall in the claimant count, from 20,800 to 15,900.
Its figures also showed the unemployment rate was 7.8% in the April to June quarter.
Encouraging news on the headline unemployment figure is unlikely to calm fears of a spike in jobless workers when the Government's austerity measures take effect.
A survey of 600 employers earlier this week by the Chartered Institute of Personnel and Development (CIPD) found a third expected to cut jobs in the next three months - the worst figure for a year and up from one in four at the end of 2009.
The Treasury itself has estimated that there will be 600,000 public sector job cuts over the next five years and experts worry this will far outweigh any rise in employment in the private sector.
The ONS data showed further pressure on wages, with average earnings up 1.3% in the three months to June, down sharply on the 2.7% previously.
This comes as Britons battle against stubbornly high inflation, which has remained above the Government's 3% target throughout 2010 so far.
There are also worrying signs for long-term unemployment, with the number of people out of work for more than a year up 33,000 to a 13-year high of 796,000 over the quarter to June.
However, the number of economically inactive workers fell further from record highs seen earlier this year, down 49,000 to 9.4 million.
The ONS added that UK job vacancies lifted by 9,000 during the three months to July, to 481,000.
This was up 51,000 on a year earlier and meant there were 1.8 vacancies per 100 employee jobs.
Unemployment in the regions between April and June was:
North East 120,000 plus 1,000 9.4%
North West 276,000 minus 20,000 8.1%
Yorkshire/Humber 244,000 minus 15,000 9.1%
East Midlands 170,000 plus 3,000 7.4%
West Midlands 221,000 minus 27,000 8.3%
East 203,000 plus 7,000 6.8%
London 383,000 plus 12,000 9.3%
South East 268,000 minus 13,000 6.1%
South West 165,000 minus 1,000 6.1%
Wales 130,000 minus 4,000 9%
Scotland 223,000 plus 7,000 8.4%
N Ireland 55,000 minus 1,000 6.6%
Vicky Redwood of Capital Economics said the latest unemployment figures were "generally positive", with the rise in full-time jobs a welcome sign for the UK.
But she said the marginal drop in the claimant count gave cause for concern.
"This might be a sign that the slowdown in the wider economic recovery is already spreading to the labour market. And with sharp public sector job cuts looming, we still think that renewed rises in unemployment lie ahead," she said.
Howard Archer, chief economist at IHS Global Insight, predicted the number of unemployed in the UK would start rising back up later this year, increasing throughout 2011 to peak at 2.85 million in 2012.
He added the wider economy may come under further pressure as consumers feel the pinch from muted wage growth and high inflation.
"With wage growth muted and a major fiscal squeeze increasingly kicking in, it is hard to see consumer spending being anything else than muted for an extended period," he cautioned.
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