UK unemployment fell by 64,000 to 1.49 million in the three months to May, official figures show.
It meant the unemployment rate fell to its lowest since 1975, at 4.5%, the Office for National Statistics (ONS) added.
But wage increases continued to fall further behind inflation.
Excluding bonuses, earnings rose by 2.0% year-on-year. However, inflation had hit an almost four-year high of 2.9% in May.
“Despite the strong jobs picture… there has been another real-terms fall in total earnings, with the growth in weekly wages low and inflation still rising,” said Matt Hughes, senior statistician at the Office for National Statistics.