The employment rate remained at a record high of 74.5%, with 31.8 million people in work between May and July - 174,000 more than the previous quarter.
A total of 1.63 million people are unemployed - a fall of 39,000 over the quarter and 190,000 down compared with a year ago, giving a jobless rate of 4.9%.
The claimant count, including Jobseeker's Allowance, jumped by 2,400 to 771,000 between July and August, the Office for National Statistics said.
Average earnings increased by 2.3% in the year to July, 0.2% down on the previous month.
Job vacancies were up 3,000 to 752,000 between June and August, which includes two months after Britain voted to leave the European Union.
Nick Palmer, ONS statistician, said: "These figures show continued labour market improvement, with the employment rate remaining at a record high and inactivity at a new record low."
The single month Labour Force Survey for July recorded an unemployment rate of 4.7%, down 0.4% compared with the month before, while the unemployment level dropped by 154,000 to 1.6 million over the period.
However, the ONS urged caution over reading too much into single-month data.
Other figures showed that the number of people classed as economically inactive dropped by 92,000 to 8.8 million in the quarter.
The number of economically inactive women fell by 74,000 to a new record low of 5.5 million.
Damian Green, Work and Pensions Secretary, welcomed the data, but said there was still more work to do.
"It's great to see another record-breaking set of figures out this month with the unemployment rate at a 10-year low and wages growing healthily.
"We know that there are fewer children living in workless households too, which underlines our efforts to help people move into employment and to build a Britain that works for everyone, not just the privileged few."
The ONS said that 79.4% of men and 69.8% of women aged between 16 and 64 were in work over the three months to July. The employment rate for women hitting its highest level since records began.
Workers employed in the public sector slipped by 13,000 to 5.3 million on the month to June, while the number of people employed in the private sector jumped by 186,000 to 26.4 million over the period.