Sir Keir Starmer has called on Prime Minister Boris Johnson to apologise for a “near collapse” in the government’s coronavirus test and trace system.
The Labour leader told the BBC ministers had “lost control of where the virus is”, making the need for further restrictions “more likely”.
He added that “fixing testing” should be the “number one priority”.
The health secretary said extra resources were being put towards speeding up test results.
Mr Hancock blamed a spike in those without symptoms seeking tests for an increase in demand, but said this had fallen in the last week or so.
But he admitted the proportion of test results being turned around within the government’s 24-hour target period “clearly needs to go up”.
It comes as the government introduces fines of up to £10,000 for people who fail to self-isolate after being ordered to do so.
Speaking on the BBC’s Andrew Marr programme, Sir Keir said Labour would support “whatever measure” ministers take to suppress virus cases.
But he added: “If I were the prime minister, I would apologise for the fact we’re in this situation with testing.
“Throughout the summer, we were saying ‘prepare for the autumn’. Instead, we had the exams fiasco.
“I would make fixing testing the number one priority, and reinstate the daily press conferences so we know what’s going on.”