Sir Patrick Vallance told ITV News that ideally 60% of the UK would become infected to ensure we were "all a bit protected".
Sir Patrick said the advice the Government is following is not looking to suppress the disease entirely but to help create a "herd immunity in the UK" while protecting the most vulnerable from Covid-19, warning "this is not a short term outbreak, this is going to go on for months."
Herd immunity occurs when a high percentage of the population gains immunity to a disease which makes it difficult for the infection to spread, because there are not many people who can be infected - it is how vaccinations work .
It gives protection to vulnerable people such as newborn babies, elderly people and those with compromised immune systems.
"What we're trying to do and we've been working on this since January to make sure we've got the right approach is do the things that matter most first and do them in the right order," he said.
Sir Patrick added: "So the measure yesterday which was to ask anybody who's got a new persistent cough or temperature above 37.8 (degrees Celsius) to stay at home for a week is a very impactful measure. Is reduces potentially the peak by about 20%.
"Then follow that up with potentially households being asked to do that for 14 days, and the peak of the infection to make sure the elderly and vulnerable are properly protected, that could reduce the death rate by 20-30%.
"Those are the measures that are most important to get out."
But the UK's approach has drawn criticism from those, including former Health Secretary Jeremy Hunt, who say the measures do not go far enough.
Many other countries, including the and , have taken the decision to close schools and universities and cancel mass gatherings - steps Sir Patrick said may "seem logical" but were "a small way to stop" the spread of the infection.
Sir Patrick said there was greater risk of catching coronavirus through contact with friends and family, but did not rule out taking more far reaching measures in the future.
"When you look at infections across whole communities, when you get up to about 60% who've had it, you get something like herd immunity which means we're then all a bit protected from it.
"So if it does get to that level that provides quite a lot of protection going forward as that may become an annual event like seasonal flu," Sir Patrick told ITV News.
Sir Patrick said it would depend on "what proportion of those who are asymptomatic and what proportion get very seriously ill" as to whether the UK had the resources to cope with 60% of the population being infected.
"We know that the people most likely to get most seriously ill are the elderly and those with pre-existing health conditions," he added.
Earlier, Mr Hunt said the UK is in a "national emergency" and that many people "will be surprised and concerned" that the UK is not moving sooner.
But Sir Patrick stood by the UK's approach.
"If you look at what other countries have done, some of them have jumped very quick on some measures that actually may be slightly less effective and aren't concentrating on the ones that really are the most impactful," he told ITV News.
"They're easy ones to go for because it sounds logical, stopping a massive event is going to be a big way to stop this. In fact it's a small way to stopit.
"It doesn't mean we won't do it at some point and there may well be a time when you need to do it anyway for things like the resilience of the healthcare system and having to support events with ambulances which is why Scotland made the decision it made yesterday.
"But most infections are going to incur from people that you know, within in small settings, family, friends and so on is the biggest route of transmission of this."
They have also been questions raised over the measures to protect those in care homes, including limiting visits to the elderly and vulnerable.
Responding to the criticism, Sir Patrick said isolation in itself brings its own dangers and enforcing more draconian measures would have to be done at the right time to avoid other complications.
He said: "We're going to be asking people to be isolated for long periods of time. And that in itself comes with risks and hazards in terms of their own health from other things.
"So doing this at the right time becomes quite important and you need to do it as the numbers increase and do it quickly and effectively at that point."
In a press conference on Thursday, Professor Whitty, said the peak of the outbreak is most likely still 10 to 14 weeks away as the Prime Minister warned families would continue to "lose loved ones before their time"
The number of people who have tested positive for the virus in the UK rose to 596 while the death toll in British hospitals stands are 10.
High-profile people to be diagnosed with Covid-19 include Arsenal head coach Mikel Arteta and BT boss Philip Jansen.
Mr Trudeau's office said he is feeling well and will continue to work.
Coronavirus: Everything you need to know