The number of people in work continued to increase - up by 42,000 to 32.39 million, although the rate remained at 75 per cent, said the Office for National Statistics.
Job vacancies increased by 20,000 to a record high of 829,000, while average earnings increased by 2.4 per cent in the year to June, down from 2.5 per cent the previous month.
The number of workers on zero-hours contracts fell by 104,000 over the past year to 780,000, the first substantial fall since the ONS started tracking the figures in 2000.
The percentage of workers employed on a zero-hours contract is now 2.4 per cent down from 2.8 per cent a year ago.
Senior ONS statistician Matt Hughes said: "The number of people in work has continued to edge ahead, though the employment rate was unchanged on the quarter.
"The growth in employment is still being driven by UK nationals, with a noticeable drop over the past year in the number of workers from the so-called A8 eastern European countries in particular."
The number of people classed as economically inactive, including students, those on long-term sick leave, taken early retirement or who have given up looking for work, increased by 77,000 to 8.7 million in the latest quarter, giving a rate of 21.2 per cent.
The claimant count, which includes people on Jobseeker's Allowance and the unemployment element of Universal Credit, increased by 6,200 last month to 906,100, almost 108,000 more than a year ago.