Unemployment falls by 65,000 between March and May to 2.58 million but the number of people claiming jobseeker's allowance last month increases by 6,100.
The number of people in employment increased by 181,000 to just under 30 million, the highest for almost four years.
But the numbers claiming jobseeker's allowance jumped by 6,100 last month to 1.6 million, including an increase of 8,000 among women to 530,700, the highest figure for 17 years.
The Office for National Statistics said the increase among women was likely to have been affected by a change in eligibility rules for lone parent income support from May.
Long-term unemployment has also increased, with those out of work for more than two years up by 18,000 to 441,000, the worst figure since 1997.
The number jobless for more than a year rose by 3,000 to 885,000, while there were just over a million unemployed 16 to 24-year-olds, down 10,000 on the three months to February.
Most age groups showed increases in employment, with a rise of 52,000 in over-65s in work to reach 929,000, the highest since records began in 1992.
The unemployment rate is now 8.1 per cent, down by 0.2 percentage points, although the jobless total is 132,000 higher than a year ago.
The biggest falls in unemployment, and increase in work, was in London, suggesting that the Olympic Games is having an impact on the figures.
16 July 2012