Unemployment fell by 121,000 to 2.12 million between March and May, official figures showed.
The number of people claiming jobseeker's allowance last month fell by 36,300 to 1.04 million, said the Office for National Statistics.
Average earnings increased by 0.3% in the year to May, 0.5% down on the previous month.
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Chancellor Rishi Sunak unveiled the economic support package for the sector on Sunday evening.
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