Speaking on Sunday, the minister again urged the public to follow the new lockdown rules as “every flex can be fatal”.
“The NHS is under very serious pressure,” he told the BBC’s Andrew Marr.
“As the chief medical officer (Chris Whitty) said, it is under the greatest pressure it ever has been, and that’s particularly true in some parts of the country but frankly it’s true right across the UK.
“And we can all do something about it. The NHS has never needed everyone to do something more than it’s needed that now, and that’s stay at home.”
Labour leader Keir Starmer said on the same programme that nurseries should “probably” be closed in England.
Hancock would not speculate on whether the lockdown rules could be strengthened, and stressed, when it came to primary schools, they were open for “key workers’ children”.
He told Sky News: “It’s always been the guidance that schools are there for key workers’ children where key workers need to have the children in school in order to be able to get to work.”
The chief executive of the College of Paramedics, meanwhile, has said that services are under “unprecedented pressure” with handover delays at a scale that “haven’t been seen before”.
Tracy Nicholls told Sky News’ Sophy Ridge On Sunday some ambulances had been left waiting outside hospitals for up to nine hours while carrying patients.
She said: “We are very used to seeing ambulance services take some strain over the winter months due to the normal pressures we would see any particular year.
“But this year particularly has seen incredible pressure because of the clinical presentation of the patients our members are seeing. They are sicker.”
She added: “We are seeing the ambulance handover delays at a scale we haven’t seen before.”
Professor Peter Horby, chairman of the New and Emerging Respiratory Virus Threats Advisory Group (Nervtag), which advises government, said lockdown rules could be tightened if it becomes clear the virus is not under control.
He told Marr: “I really hope people take this very seriously. It was bad in March, it’s much worse now.
“We’ve seen record numbers across the board, record numbers of cases, record numbers of hospitalisations, record numbers of deaths.
“We are now in the eye of a storm, so to speak, and people need to take this extremely seriously.”
Starmer said the current lockdown rules “may not be tough enough”.
He told the BBC: “They are tough and they’re necessary. They may not be tough enough.
“In a sense, I think the most important thing is people get that message about stay at home.
“And it’s up to the government to put that message out there the whole time. We’ve had mixed messages I’m afraid for the last nine months which is why we’ve got a problem.
“I would like to see the Prime Minister out there every day with a press conference making sure that message is absolutely getting through.”