It could be "six months or longer" until the UK is back to normal life if Brits don't comply with social distancing measures.
Housing secretary Robert Jenrick spoke to press along with Jenny Harries, the deputy chief medical officer for England at Sunday's daily briefing.
Dr Harries said we could be looking at six months or longer under coronavirus lockdown.
"We anticipate our numbers will get worse over the next week, possibly two, and then we are looking to see whether we have managed to push that curve down and we start to see a decline," she said.
"This is not to say we would be in complete lockdown for six months, but as a nation we have to be really, really responsible and keep doing what we're all doing until we're sure we can gradually start lifting various interventions which are likely to be spaced - based on the science and our data - until we gradually come back to a normal way of living."
There will be reviews of existing lockdown measures every three weeks to re-evaluate when Covid-19 will peak in Britain.
Local authorities are collaborating with the NHS to lead the UK's response to the health crisis, including "some of the finest military experts in the world".
The government is ensuring the NHS has sufficient Personal Protective Equipment (PPE) including supplying 170 million masks and 42 million pairs of gloves to more than 58,000 healthcare providers and NHS trusts.
A national supply distribution response team has been established and will be supported by the armed forces, working around the clock to deliver the equipment to "those who need it most".
"We simply cannot and should not ask people to be on the frontline without the right protective equipment," Mr Jenrick says.
"We will not stop until we have got you the equipment you need."
More than one million people considered highly at risk of coronavirus have received letters telling them to stay home for the next 12 weeks. The NHS will deliver essential medication and food items to people who don't have family or friends to collect goods for them.
Three quarters of a million people have signed up to volunteer with the NHS during the pandemic.
The number of people who have died with the virus in the UK has reached 1,228 - an increase of 209 since Saturday.
More than 127,000 Brits have now been tested for Covid-19, with 19,522 confirmed cases.