Unemployment claims surged by a record 856,000 from March, the Office for National Statistics said in a statement.
The ONS added that the number of unemployed jumped by 50,000 to 1.3 million people in the first quarter, compared with a year earlier.
"I certainly won't be able to protect every job, and every business... there will be more hardship to come," finance minister Rishi Sunak said in parliament Tuesday.
Britain imposed a lockdown on March 23 to halt the spread of the virus, and launched a furlough jobs retention scheme under which the government is paying the bulk of wages.
UK furloughing is supporting eight million jobs at a cost of £11.1 billion ($13.4 billion, 12.2 billion euros) to the taxpayer, the Treasury said Tuesday.
But many workers have been laid off in recent weeks, with companies including British Airways preferring to axe thousands of staff despite the state helping to safeguard jobs.
Chancellor of the Exchequer Sunak on Tuesday said the lockdown was "having a very significant impact on our economy.
"We are likely to face a severe recession, the likes of which we haven't seen and of course that will have an impact on unemployment."
He added: "The longer the recession, it is likely the degree of that scarring will be greater."
Britain's lockdown is just starting to be eased, while the government has said that under the furlough scheme it will continue to pay up to 80 percent of wages until October.
"It is not obvious that there will be an immediate bounceback" in the economy, Sunak said.
"It takes time for people to get back to the habits they had, there are still restrictions in place."
ONS statistician Jonathan Athow said Tuesday's data also showed the number of employees on company payrolls had dropped "noticeably, and vacancies were sharply down too, with hospitality" falling by the sharpest amount.
Analysts stressed that the labour market would deteriorate even more sharply in the coming months.
Andrew Wishart at research group Capital Economics said the UK unemployment rate would hit 6.0 percent in the coming months" and could reach as high as 9.0 percent.