UK unemployment fell by 65,000 to 1.36 million in three months to June – the lowest for more than 40 years, official figures from the Office for National Statistics (ONS) show.
They also show a rise in productivity, but a slowdown in wage growth.
Wages, excluding bonuses, grew by 2.7% in the three months to June, compared with a year ago.
The ONS figures also showed the number of European Union nationals working in the UK fell by a record amount.
The fall was the largest annual amount since records began in 1997. It continues a trend seen since the 2016 Brexit vote.
The unemployment rate fell to 4% in the quarter to June. That was the lowest since the three months to February 1975, beating the figure expected by economists.
The drop came despite a smaller-than-expected number of jobs created over the three-month period of 42,000.
On productivity, the ONS also said output per hour worked grew by 1.5%, the biggest rise since late 2016.
The official figures also slowed a fall of 104,000 in the number of those on of those on “zero-hours contracts” in their main job, to 780,000.
It also said the number of people aged from 16 to 64 years who were not working, or looking for work, or available to work – what is known as “economically inactive” – increased by 77,000 from the first quarter of the year.