Other "wartime" measures are to include using car plants to make ventilators and hotels as hospitals.
He told the BBC the advice will not come into force just yet but when it does it will last "a very long time".
Wartime-like measures will ask car makers to produce medical equipment and turn hotels into hospitals, he said.
"Every single person in this country is going to be affected," he warned.
Over-70s - and younger people with certain health conditions - will need to remain at home and have groceries and vital medication delivered, the health secretary said.
The Scottish government has set out its interpretation of the strategy, saying it had no plans to isolate the elderly, but would instead "ask them to reduce social contact".
Jeane Freeman, Mr Hancock's counterpart in Scotland, said: "We don't want people who are elderly to be stuck in their homes alone not contacting anyone, with their families not able to be in touch with them and to help them.
The Scottish government has also published its guidance that gatherings of 500 people or more should not take place in Scotland.
Although it does not have the power to call off events, it has urged organisers to "act responsibly" in cancelling large gatherings from Monday to help the efforts of emergency services.
All the UK deaths from the virus so far have been among people aged over 60 or with underlying health conditions.
Mr Hancock told the BBC's Andrew Marr people without symptoms would be able to visit older relatives and friends so long as they stayed two metres - or six feet - apart from them.
He said car manufacturers, weapon makers and army suppliers would be asked to change their production lines to make ventilators for use in hospitals treating coronavirus - which can cause severe breathing problems.
Plea for ventilators
The health service is to stop non-urgent surgery and implement a huge training programme to retrain medics from other specialisms to treat those who become seriously ill with the Covid-19 disease.
"We will stop at nothing to fight this virus and I think people have got the impression otherwise," Mr Hancock said.
Prime Minister Boris Johnson is to hold a conference call with industry leaders later to discuss the need to help produce medical equipment "at speed", Mr Hancock said.
What is a ventilator?
- A ventilator is a machine that helps a person breathe by getting oxygen into the lungs and removing carbon dioxide
- Ventilators can be used to help a person breathe if they have lung disease or another condition that makes breathing difficult. They can also be used during and post-surgery
- A tube, connected to a ventilator machine, is placed in a person's mouth, nose or through a small cut in the throat (called a tracheostomy)
Mr Hancock said there were 5,000 ventilators available at the moment, but that many times that number would be needed.
Work is also under way to buy up thousands of private hospital beds to boost NHS capacity should it be needed and the possibility that empty hotels may be requisitioned has not been ruled out.
Mr Hancock declined to give details of when the over-70s would be asked to self-isolate or how long the advice would last, saying: "We want to be ready to say that when we judge, based on the scientific advice, that the time has come."
"We know that when you ask people to do this sort of thing that they can tire of it, it also has negative impacts," he added.
Mr Hancock earlier used an article in the Sunday Telegraph to liken the coronavirus crisis to World War Two.
He wrote that, despite the Blitz, the UK "pulled together in one gigantic national effort" and that the same must happen once more.
It came as the government's strategy was criticised by some scientists, who wrote to ministers urging them to introduce tougher measures to tackle the spread of Covid-19.
"Of course there is a scientific debate around scientific concepts but I want to be absolutely crystal clear, we will do what is necessary," Mr Hancock said.
Shadow health secretary Jonathan Ashworth said the public did not want ambiguity from the government.
"People just want clear advice. The prime minister should be out there daily speaking to the nation and explaining why things are changing," he told Sky News' Sophy Ridge.
The total number of confirmed coronavirus cases in the UK has reached 1,206, after 34 new cases were announced in Wales and 32 in Scotland.The latest figures for England and Northern Ireland are expected shortly.
A total of 21 people have died since the beginning of the outbreak.
Only patients in hospital are currently being tested for the virus.
An emergency bill giving the government temporary powers to tackle the outbreak will be published next week.
Labour leader Jeremy Corbyn has asked for "urgent sight" of the draft laws and for a meeting with the prime minister to discuss the crisis.
His party has already called on the government to publish the scientific modelling and data that it is using to inform its approach.
Why and when should vulnerable self-isolate?
Shielding the vulnerable and elderly will be an essential part of the government's strategy when cases are rising rapidly - it was one of the decisions signed off at an emergency Cobra meeting on Thursday.
Half of the overall cases are expected within a period of a few weeks, with 95% in a period of around 10 weeks.
So officials will ask those at most risk of developing severe illness to stay at home.
They believe if they get the timing right and people adhere to it the move could reduce the number of deaths by up to a third.
But it of course carries its own risks - mentally and physically.
They believe the longest they could ask people to do this for is around 12 weeks or so.
That's why it's essential people don't go too soon. At the moment the vulnerable groups should be protected to a degree by the fact that the small number of people with the virus should be self isolating.
But the officials recognise that individuals will make their own decisions about when to start.
Meanwhile, a new public information campaign is to be launched featuring the UK government's chief medical adviser Prof Chris Whitty.
In other developments:
- The Foreign Office advised against all but essential travel to the whole of Spain after restrictions were put in place by the Spanish government
- Around 600 Britons are among the passengers stranded on a Fred Olsen cruise ship that has been unable to dock in the Bahamas after five people on board tested positive for the coronavirus
- Airlines warned the UK's aviation industry may not survive the coronavirus pandemic without emergency financial support
- The US will extend its European coronavirus travel ban to include the UK and Republic of Ireland from 04:00 GMT on Tuesday
- As a result, the Foreign Office is advising against all but essential travel to the US, effective from midnight on Monday EST (04:00 GMT on Tuesday)
- The Austrian government has sent text messages to its citizens in the UK, saying it is "not convinced" by the UK's anti-virus measures and urging them to return to Austria
- The Jet2 airline has stopped all flights to Lyon, Grenoble, Paris and Nice with immediate effect due to travel restrictions enforced by the French government
- Andy Burnham, the Labour Mayor of Greater Manchester, has called for daily televised press conferences led by the chief medical officer to take place from today