Unemployment increased by 25,000 between April and June to 1.85 million, official figures have shown.
The number of people claiming jobseeker's allowance last month fell by 4,900 to 792,400, the Office for National Statistics said.
Average earnings increased by 2.4% in the year to June, 0.8% down on the previous month.
The latest figures show the second consecutive monthly rise in unemployment after two years of decline in the number of people out of work.
More top news
The Democratic presidential candidate may also have shown his cards on his choice of running mate.
The US president also shared a post on Twitter accusing Dr Anthony Fauci of misleading the public over hydroxychloroquine.
Fears over an impending second wave of coronavirus dominates Wednesday’s front pages.