Significant problems are being reported after an "incredible" number of benefit claims in recent days due to the economic fall-out of the coronavirus.
At one point on Tuesday more than 100,000 people were trying to verify online applications and others spent hours trying to phone welfare staff.
Many gave up after long phone queues and then being rejected by the system.
The Department for Work and Pensions said it was redeploying existing staff and hiring others to cope with demand.
Research by the BBC suggests that pressure on the benefits system started to build in the middle of last week, shortly after the government introduced the first set of restrictions and then surged markedly on Tuesday after the prime minister ordered most businesses to close on Monday night.
New claimants, many of them self-employed and facing a dramatic fall in income, took to social media to highlight the problems.
One user posted a screenshot on Twitter of their application which said that "due to an incredible volume of new users," there were 105,563 people ahead of them in an online queue to verify their identity, a basic requirement of applying for any benefit.
Jonathan Hume estimates he has called the Universal Credit hotline somewhere between "80 and 100 times" since Friday.
His contract as a research associate at the University of Manchester came to an end earlier this month and the 32-year-old needs to contact a benefits official to process his claim.
"I just can't get through at all," Mr Hume told BBC News.
"Most of the time, the line just drops instantly.
"On another few times when I've got through, I've been on hold for two hours and then my network has just cut me off.
"It's infuriating and stressful as, until it's sorted, I have no income."
Tens of thousands of people have become eligible to apply for Universal Credit in recent days due to the economic consequences of Covid-19.
In a statement on Monday night, the Department for Work and Pensions (DWP) had urged applicants to use their online system after days of people using social media to complain about being unable to get through to their telephone support lines.
One user reported spending more than 15 hours in total over three days waiting to speak to a benefits official, while several others posted screenshots of phone calls lasting more than two hours.
Some claimants struggled for hours to even connect to the system.
The government announced on Monday that all job centres would be closed for everyone but "the most vulnerable claimants who cannot access DWP services" by other means - urging claimants to use online and telephone support.
In a statement, the DWP said it was taking "unprecedented" action to ensure people received the support they needed.
"Around 10,000 existing staff will be moved to process new claims, with 1,000 already in place.
"In addition, the department is expecting to recruit 1,500 extra people to aid the effort," the statement continued.