Speaking at the daily Number 10 press conference today, Mr Hancock urged people to use the NHS if they needed it after a drop-off in attendance at A&E during the crisis.
He announced that 21,092 people have now died in UK hospitals after testing positive for Covid-19, an increase of 360 fatalities from hospitals registered since yesterday. This was the lowest total since March 30 but is thought to be artificially low because of lower rates of reporting.
Chief medical officer for England Professor Chris Whitty said the country is not "consistently" past the peak of coronavirus deaths. He said there was an "artificial drop" over the weekend typically seen because of lower notification rates.
"Nevertheless the trend overall ... is a gradual decline but we're definitely not consistently past the peak across the whole country at this point in time," he added.
Mr Hancock announced that families of NHS and social care staff who die from coronavirus in the course of "essential frontline work" will receive a £60,000 payment.
And he revealed that some NHS services which had been paused due to the coronavirus outbreak will be restored from tomorrow (Tuesday).
The Health Secretary said there were 3,190 spare critical care beds - adding "42 per cent of oxygen-supported beds in the NHS now lie empty".
"In most parts of the country, the number of people in hospital with coronavirus is beginning to fall."
He said: "As the number of hospitalisations from coronavirus begins to fall, I can announce that, starting tomorrow, we will begin the restoration of other NHS services - starting with the most urgent, like cancer care and mental health support.
"The exact pace of the restoration will be determined by local circumstances on the ground, according to local need and according to the amount of coronavirus cases that that hospital is having to deal with.
Mr Hancock said the number of patients attending A&E had fallen to 221,000 in the last week from 477,000 in the same week last year.
"Some of this drop is due to lower road traffic and people following the social distancing rules. Some of it will be due to people accessing the NHS in ways that work better for them, like online or through pharmacies, and that's a good thing.
"But in some cases we know that the drop is due to people not coming forward and using the NHS for critical things that matter. Our message is that the NHS is open. Help us to help you."
Mr Hancock told the press conference:
- There have been 719,910 tests for coronavirus so far in the UK, including 37,024 on Sunday
- 157,149 people have tested positive, an increase of 4,310 cases since Sunday
- 15,051 people are in hospital with coronavirus, down from 15,239 on Sunday
- 21,092 people have died in hospital with coronavirus, an increase of 360.
Mr Hancock said: "We must never lose sight of the human cost of coronavirus and the pain and the grief that it causes."
Earlier Boris Johnson said the UK is at the point of "maximum risk" in its battle with coronavirus, as he acknowledged frustrations over the continuing lockdown but insisted he would not risk a second peak in the disease by relaxing restrictions too quickly.
As the Prime Minister returned to take charge of the Government's response to the coronavirus crisis following his recovery from Covid-19, he said there are signs that the UK is "passing through the peak" of the outbreak and "coming now to the end of the first phase of this conflict".
Comparing the disease to a mugger, he said: "This is the moment when we have begun, together, to wrestle it to the floor."
But he said it is also the moment of maximum risk because of the danger that people would look at the "apparent success" and "go easy" on social distancing measures.
It remains the "biggest single challenge this country has faced since the war", he said, and "every day I know that this virus brings new sadness and mourning to households across the land".
More than 20,000 people have already died with the disease in hospitals, with the true death toll including care homes and other settings likely to be far higher.
Speaking from a podium in Downing Street, Mr Johnson acknowledged the pressure to lift some of the draconian restrictions imposed on British people and businesses.
He said: "I want to get this economy moving as fast as I can" but "I refuse to throw away all the effort and the sacrifice of the British people and to risk a second major outbreak and huge loss of life."
The Prime Minister has been under intense pressure to set out how the lockdown will be lifted. He indicated that it would be a gradual process and promised the "maximum possible transparency" with efforts to seek consensus across party lines.
He said: "When we are sure that this first phase is over and that we are meeting our five tests - deaths falling, NHS protected, rate of infection down, really sorting out the challenges of testing and PPE, avoiding a second peak - then that will be the time to move on to the second phase in which we continue to suppress the disease and keep the reproduction rate - the R rate - down, but begin gradually to refine the economic and social restrictions and one by one to fire up the engines of this vast UK economy.
"And in that process difficult judgments will be made and we simply cannot spell out now how fast or slow or even when those changes will be made, though clearly the Government will be saying much more about this in the coming days."