Currently almost 5,683 people have tested positive for the respiratory disease in the UK, while 281 have died.
Monday will see MPs return to the House of Commons after the weekend to debate the government's Coronavirus Bill in all its stages, before it goes to the House of Lords and becomes law by the end of this week.
Under the proposals, airports could close and police could be given powers to force people with virus symptoms to isolate.
The Coronavirus Bill - totalling 329 pages - enables action to increase the available health and social care workforce, ease the burden on frontline staff, slow the spread of the virus, manage the deceased with respect and support people through the crisis.
The legislation, published on Thursday, set out powers for the police to detain people suspected of having coronavirus and send them for testing. People who fail to do so could be fined up to £1,000.
Other measures include powers for ministers to write to an operator of a port requiring their operation be suspended and for events or gatherings to be cancelled.
Food suppliers would also have to provide information to the appropriate authority if all or part of a food supply chain is being disrupted or is at risk of disruption.
The legislation, which is time-limited for two years, also modifies current laws to enable coroners to conduct an inquest without a jury for anyone whose death was caused by Covid-19.
Number 10 confirmed that the Government would introduce an amendment to the Bill on Monday to ensure it has to be renewed every six months.
A spokesperson added: "The two-year time limit for the Act overall remains in place, and not all of the measures will come into force immediately."
Local authorities will also be given the power to decide what happens to dead bodies and their disposal to ensure excess deaths do not overwhelm the system, and funeral directors acting on behalf of a family will be able to register a person's death.
What is social distancing?
Meanwhile, Boris Johnson is facing mounting pressure to order stricter measures after thousands of people ignored calls for “social distancing” to slow the coronavirus pandemic.
The Prime Minister said he will be thinking “very, very actively” about what steps to take if people continue to gather in large numbers in defiance of calls to stay apart.
There was anger among MPs at scenes over the weekend of crowds flocking to parks, markets, beaches and beauty spots.
Speaking on Monday, the Health Secretary called people ignoring Government advice by leaving their homes to socialise "selfish" and said they could be costing lives.
Matt Hancock said he would not rule out a full lockdown just as Downing Street also said Boris Johnson would not hesitate to take further action if stricter measures were needed to enforce social distancing.
Conservative former Cabinet minister Julian Smith said he would support “any measure” the Government brought forward to force people to comply with the guidance.
For Labour, shadow health secretary Jonathan Ashworth said ministers should be making “immediate preparations” for the “next stage” while learning from other European nations.
Coronavirus: Everything you need to know:
The calls came as an 18-year-old was thought to have become the youngest victim of the virus in Britain as the number of deaths in the UK rose to 281.
There are growing fears that Britain is on a similar trajectory to Italy – scene of the world’s worst outbreak – where the death toll passed 5,000 over the weekend.
The Italian government was one of a number of European countries to announce new or extended restrictions – with Germany banning public gatherings of more than two people not from the same household.
Mr Johnson warned that the NHS could be “overwhelmed” in the same way as the Italian healthcare system has been, if the the spread of the virus in the UK is not curbed.
But at his daily No 10 press conference on Sunday, Mr Johnson indicated he was reluctant to ban people from going outside for a walk or to exercise because of the physical and mental health benefits, as long as they acted responsibly.
The Government later issued updated guidance making clear that essential travel did not include visits to “second homes, camp sites, caravan parks or similar, whether for isolation purposes or holidays”.
However among some MPs there was a clear mood for firmer action amid fears that further delay would cost lives.
Mr Smith, the former Northern Ireland secretary, said: “Many people have recklessly ignored government advice this weekend.
“I will support any measure the Government needs to force people to follow the guidelines designed to protect NHS staff and UK citizens’ lives.”
For Labour, Mr Ashworth said: “We urge the Government to make immediate preparations for the next stage and learn lessons from other European nations.
“If voluntary social distancing measures are not adhered to, the Government must bring forward their plans for stronger action.”
Labour MP Rosena Allin-Khan, who also works as an A&E doctor at St George’s Hospital in south London, also bitterly attacked the Government’s approach.
She said her latest shift had been a “deeply, deeply eye-opening” experience with previously fit and healthy people in their 30s and 40s “attached to machines, fighting for their lives”.
“The Prime Minister has been blase about this from the start, waiting for others to make decisions so he doesn’t have to. It is costing lives,” she said.
“Enough is enough.
"The NHS cannot cope and it won’t be long before doctors have to choose between who lives and who dies.”
While people were heading to open spaces, there were signs that city and town centres were closing down with McDonald’s, John Lewis, Primark and Timpson among the high street chains to announce they were closing their doors.
The Government said it would ensure those without families and friends to support them would continue to receive food and medicines, with the military helping to organise deliveries.
Schools across the country will be opening their gates only to the children of key workers considered essential to the running of the country, with apparent confusion over how many will be admitted.
Education Secretary Gavin Williamson appealed to parents to keep their children at home unless their job is “critical” in the response to the coronavirus.
“This will help to halt the spread of the virus, protect the NHS and save lives,” he said.
“We will be closely monitoring what is happening in schools and will ensure they get the support they need in the weeks and months ahead.”