Unemployment fell by 39,000 in the three months to July to stand at 1.63m, the lowest figure since 2008.
Figures from the Office for National Statistics show employment rose by 174,000 over the same period to 31.77m.
There were 23.25m people working full-time, up by 434,000 compared with May to July 2015. Another 8.51m were working part-time, up by 126,000 year-on-year.
The employment rate was 74.5 per cent, the joint highest since comparable records began in 1971. The unemployment rate was 4.9 per cent, down from 5.5 per cent a year earlier. The last time it was lower was July to September 2005.
Average weekly earnings, including bonuses, increased by 2.3 per cent compared with a year earlier. Excluding bonuses, average earnings rose by 2.1 per cent.
Neil Carberry, director of people and skills at the Confederation of British Industry, said: "With much of the data still pre-referendum, it's too early to make any assumptions about the effect of June's vote to leave the European Union on the UK's labour market.
"But the strength of employment growth in the first half of this year is encouraging and highlights the resilience of the UK's flexible labour market.
"Maintaining this flexibility as we navigate the challenges and opportunities the country faces following the EU Referendum will be vital for our future prosperity, pay and job creation."