Health Secretary Matt Hancock said it is a "very big ask", but it is a measure which is for their own "self-protection".
In an acknowledgement of the almost wartime measures being introduced, Mr Hancock said the steps are "very, very significant and they will disrupt the ordinary lives of almost everybody in the country".
The gearing up of the Government's efforts comes as the UK's Covid-19 death toll rose on Saturday from 11 to 21, while the number of people testing positive for the disease passed the 1,000 mark.
Mr Hancock said that people aged over 70 will be asked in the coming weeks to self-isolate for up to four months, in order to protect them from the virus.
Asked if that was in the Government's plan, he told Sky's Sophy Ridge On Sunday: "That is in the action plan, yes, and we will be setting it out with more detail when it is the right time to do so, because we absolutely appreciate that it is a very big ask of the elderly and the vulnerable, and it's for their own self-protection."
Pressed on when the measure will be introduced, he said: "Certainly in the coming weeks, absolutely."
He said coronavirus is "a very significant challenge" that will "disrupt the lives of almost everybody" in the UK.
"The measures that we're taking, the measures that we're looking at taking, are very, very significant and they will disrupt the ordinary lives of almost everybody in the country in order to tackle this virus," he said.
The Prime Minister Boris Johnson will personally urge manufacturers to shift their production lines to build ventilators, as the NHS prepares for a significant increase in cases of Covid-19.
Mr Hancock said: "The thing the NHS needs now more than anything else is more ventilators. We've been buying as many as we can but we need to produce more too."
He said he could not make guarantees that everyone who requires a ventilator will get one, saying: "We don't make guarantees in healthcare."
The Health Secretary said a Bill setting out emergency powers to deal with the outbreak will be published on Thursday, and details of what the powers will include will be shared on Tuesday.
Mr Hancock said ministers are yet to make a decision on whether to ban gatherings of over 500 people in the rest of the UK, after Scotland said it would bring in restrictions from Monday.
"We are absolutely ready to do that as necessary," he said, but he pointed towards a Cobra meeting being held on Monday when asked when the decision will be made.
The Government is in talks with private hospitals about the possibility of taking over beds, in a further sign of the pressures that will face the health service at the peak of the coronavirus outbreak.
Mr Hancock said: "Our generation has never been tested like this.
"Our grandparents were, during the Second World War, when our cities were bombed during the Blitz.
"Despite the pounding every night, the rationing, the loss of life, they pulled together in one gigantic national effort.
"Today our generation is facing its own test, fighting a very real and new disease."
The increase in activity came after 10 more patients died in England after testing positive for Covid-19, while the US government imposed a travel ban on the UK and Ireland in response to the coronavirus pandemic.
Experts on the UK's Scientific Advisory Group for Emergencies (Sage) set out the need for extra action to slow the spread of the disease.
The panel advised that the next interventions "will need to be instituted soon".
There could also be a shift to household isolation rather than individual self-isolation.
Mr Hancock said he was "confident" shops will not run out of food but could not guarantee it, and warned the Government could take further action.
Asked if food supply might be at risk, the Health Secretary told Sophy Ridge: "No, one of the things we are confident about is that the food supply will continue."
There have been 1,140 positive tests for coronavirus in the UK as of 9am on Saturday, up from 798 at the same time on Friday.
At a press conference on Saturday, US President Donald Trump, who has tested negative for the virus, announced the extension of his travel restrictions to cover the UK and Ireland.
The changes will come in at midnight on Monday night in the eastern US.
Downing Street said Mr Johnson and the president spoke on Saturday evening and "the Prime Minister set out the science-led approach the UK is taking".
On Monday the Prime Minister will urge manufacturers to join a "national effort" to produce equipment for the NHS.
Engineers have already been asked to draw up plans to quickly produce more ventilators in the UK, amid concerns that critical care facilities will come under intense pressure as the Covid-19 crisis intensifies.
Negotiations are also taking place with private health firms about access to their hospital beds.
NHS chief executive Sir Simon Stevens said: "We need every part of society and every industry to ask what they can do to help the effort."
Whitehall sources have already indicated that mass gatherings could be banned from next weekend.
Other measures, including school closures, have also been considered as an option to combat the spread of the virus.
Northern Ireland's First Minister Arlene Foster, who has attended the Cobra meetings formulating the UK's response, suggested that schools would need to be closed for four months if that step was taken.
Meanwhile, a newborn baby in England who has tested positive for coronavirus is likely to be one of the world's youngest patients with the disease.
The infant and its mother both tested positive at a north London hospital and staff who had contact with them have been advised to self-isolate.
The UK's approach to developing "herd immunity" against Covid-19 has been called into question.
In an open letter, a group of 229 scientists from UK universities argued that "going for 'herd immunity' at this point does not seem a viable option, as this will put NHS at an even stronger level of stress, risking many more lives than necessary".
A Department of Health and Social care spokesman said: "Herd immunity is not part of our action plan, but is a natural by-product of an epidemic.
"Our aims are to save lives, protect the most vulnerable, and relieve pressure on our NHS."