Sarah-Jane Marsh, the director of testing at NHS Test and Trace, apologised for the problem on Tuesday morning.
“All of our testing sites have capacity, which is why they don’t look overcrowded, its our laboratory processing that is the critical pinch-point. We are doing all we can to expand quickly,” she said.
It came after a dramatic spike in the number of new cases were reported across the country.
There were a further 2,948 lab-confirmed cases in the UK as of 9am on Monday, following the 2,988 reported on Sunday, which was the largest daily figure since May.
Speaking to the Commons health committee on Tuesday, Hancock said the government was working “incredibly hard” to make sure people could get a test.
“We are doing everything we can, we have had these operational issues,” he said.
“We have had a problem with a couple of contracts.
“It’s a matter of a couple of weeks until we can get all of that sorted, in the short term, in the immediate term, we’ve already put in certain solutions to make sure people don’t have to travel more than 75 miles.
“I appreciate 75 miles is far longer than you would want to go and indeed the vast majority of tests are much closer than that.”
Hancock also warned the public not to become “relaxed” about the virus and that “all options” remained on the table if cases continued to rise.
“We have seen in other countries if you don’t take a second spike seriously then it can it lead to very serious problems,” he said.
Earlier on Tuesday England’s chief medical officer Chris Whitty echoed concerns raised by his deputy Jonathan Van-Tam.
“We have, through the extraordinary efforts of the whole population, got Covid rates right down,” Whitty said on Twitter.
“They are now rising again especially in those aged 17 to 29. If we stop social distancing Covid comes back. We all need to protect others.”
It has been reported the government is considering reducing the maximum number of people who can legally gather in a private home in England to suppress the rise in cases.
Under current rules it is illegal for more than 30 people to meet in a house. Anyone caught breaking the law is subject to a £100 fine, doubling on each subsequent offence up to £3,200