Unemployment fell by 52,000 to 1.64m between April and June, according to official figures.
Data from the Office for National Statistics covering the run-up to the EU referendum shows employment increased by 172,000 compared with January to March to stand at 31.75m.
The unemployment rate was 4.9 per cent, down from 5.6 per cent a year earlier. The employment rate was 74.5 per cent, the highest since comparable records began in 1971.
In July, the first month after the Brexit vote, the number of people claiming Jobseeker's Allowance fell by 8,600 compared with June to 763,600.
Elsewhere, wages excluding bonuses rose by 2.3 per cent in the three months to June compared with a year earlier. Earnings including bonuses were up by 2.4 per cent.
Commenting on the figures, Anna Leach, CBI head of economic analysis and surveys, said: "Ahead of Britain's vote to leave the EU, the UK's jobs market remained in rude health, though vacancies have continued to tick down since the beginning of the year.
"The Bank of England was right to act swiftly to shore up confidence and keep money flowing through the economy. But businesses now need the Government to make ambitious decisions in the Autumn Statement that will secure the UK's economic future as changes to trade, regulation and access to skills loom on the horizon."