Video report by ITV News Business and Economics Editor Joel Hills
In the past month alone, 74,000 jobs were lost.
The increase was not as big as many feared, however, because large numbers of firms have put employees on the government-backed furlough scheme.
The ONS said the pace of job losses appeared to have slowed in June, with claims under Universal Credit by the unemployed and those on low incomes falling by 28,100 between May and June to 2.6 million.
But the claimant count has more than doubled since March – soaring 112.2% or by 1.4 million – in a sign of the mounting jobs crisis.
What do the statistics show?
The number of paid employees fell by 1.9% year on year in June to 28.4 million
The number of paid employees fell by 0.3% compared with the previous month
The ONS said unemployment fell 17,000 between March and May to 1.35 million, with the rate unchanged at 3.9%.
Experts said this masked a fall in employment, down 126,000 in the quarter to 32.95 million, with the rate dropping to 76.4%.
Commenting on Thursday's figures, Business Secretary Alok Sharma said many people are facing a “very, very difficult” time.
HR consultant and employment lawyer Amanda Lennon gives her advice to those worried about their future:
“I think the best thing we can do is continue to open up the economy in a phased manner, a cautious manner, and get businesses up and running again,” Mr Sharma told BBC Radio 4’s Today programme.
Shadow chancellor Anneliese Dodds said the latest unemployment figures underlined the need for continuing government support to those sectors particularly hard hit by the coronavirus crisis.
“We do think that for particularly badly affected sectors there does need to be continuing support, otherwise we will see extra waves of people potentially moving into unemployment or economic inactivity," she told the Today programme.
Jonathan Athow, deputy national statistician at the Office for National Statistics (ONS), said:
“As the pandemic took hold, the labour market weakened markedly, but that rate of decline slowed into June, though this is before recent reports of job losses.
“There are now almost two-thirds of a million fewer employees on the payroll than before the lockdown, according to the latest tax data.
He added: “There are now far more out-of-work people who are not looking for a job than before the pandemic.”
The figures show that vacancies fell 463,000 between March and May to a record low of 333,000 as companies froze hiring in the face of the pandemic.
The pace of job cut announcements has also showed no sign of slowing down in recent weeks, with some 75,000 job losses announced last month alone, according to recent analysis by the PA news agency.
This points to further grim jobless figures in the months to come.
The ONS data also showed pressure on wages, with average weekly wages including bonuses down 1.2% year over year in May – a sign of the impact of millions of furloughed workers on 80% pay.
Mr Athow said: “Pay is now falling on most measures, with many furloughed workers not having their wages topped up by their employers.”
Matthew Percival, director for people and skills at the CBI business group, said:
“These figures show serious difficulties for hundreds of thousands of people, but unfortunately this is still only the beginning of the impact on the labour market.
“Flattening the unemployment curve will remain paramount.”