Sterling increased sharply on the news, reaching an eight-day high against the dollar moving above $1.23.
The Office for National Statistics (ONS) figures for June to August showed 31.81 million people were in work, 560,000 more than the same period last year.
The employment rate – the proportion of people aged 16 to 64 who were in work – was 74.5%, the joint highest since records began in 1971.
There were 1.66 million unemployed people during the period, 10,000 more than for March to May but 118,000 fewer than for a year earlier.
The unemployment rate was 4.9%, unchanged from the previous quarter, but down from 5.4% for a year earlier.
Wage growth fell slightly to 2.3%.
Ben Brettell, senior economist at Hargreaves Lansdown, said: “The UK’s labour market is showing remarkable resilience despite Brexit-related uncertainty, with employment at an all-time high and the jobless rate at an 11-year low.
“Today’s release is the latest piece of evidence which shows the economy has fared better than expected since June’s referendum. A survey released on Monday showed UK consumers were at their most optimistic for five years – though sentiment in largely pro-Remain London fell slightly.
“Since the vote to leave the EU, economists and commentators have been forecasting a sharp rise in unemployment as the uncertainty affects firms’ hiring decisions. The Bank of England expects a rise to 5.5% once the full effect filters through. Yet for now, the UK labour market sails serenely on.”