The number of workers on UK payrolls fell 650,000 in June, official figures indicate.
The number of people claiming work-related benefits - including the unemployed - was 2.6 million.
However, the increase was not as big as many feared, because large numbers of firms have put employees on the government-backed furlough scheme.
Economists say the full effect on employment will not be felt until the scheme ends in October.
"Despite the lack of overall increase in the number of unemployed, the estimated number of people unemployed aged 16 to 24 years increased by 47,000 on the year while other age groups remained steady," said the Office for National Statistics (ONS).
The ONS added that a larger than usual number of those losing their jobs were not currently looking for another one and were therefore economically inactive rather than unemployed.
"In addition, an increased number of respondents who were previously unemployed have moved to economic inactivity," it said, "suggesting that some who were previously unemployed are no longer looking for work."