The Prime Minister set out what he called “the first sketch of a road map for reopening society”. But social distancing rules will still have to be followed and there will be bigger fines for those who breach them.
Mr Johnson said: “You must obey the rules on social distancing.
“To enforce those rules we will increase the fines for the small minority who break them.”
Fines for flouting coronavirus regulations will rise from £60 to £100.
Payment of the fine within 14 days will reduce the sum to £50, up from £30.
Boris Johnson has unveiled bigger fines for people who break social distancing rules
Repeat offenders will see the fine double for each subsequent breach to a maximum of £3,200.
It is unclear whether this applies to England and Wales or England only.
In his speech, the Prime Minister announced a new Covid Alert System determined by the reinfection rate and the number of cases.
The alert levels will be one to five and the higher the level, the tougher social distancing measures will have to be.
Mr Johnson said the UK had been in Level Four but “we are now in a position to begin to move in steps to Level Three”.
In a slight easing of the strict lockdown, people who cannot work from home are being encouraged to go to work from Monday.
But they should avoid public transport if possible.
People can take unlimited outdoors exercise from Wednesday including playing sports, but only with members of their household.
Sunbathing in local parks will also be allowed as well as driving to other destinations.
Schools may begin to reopen by June 1 at the earliest along with the phased reopening of shops.
And at least some pubs, restaurants, hotels and other public places could start to reopen in July at the earliest “if and only if the numbers support it”.
The Prime Minister said the coronavirus death toll has been “tragic”.
But he added that obeying the lockdown measures for almost two months had helped prevent a worst case scenario of 500,000 deaths.
Mr Johnson said: “It is a fact that by adopting those measures we prevented this country from being engulfed by what could have been a catastrophe in which the reasonable worst case scenario was half a million fatalities.
“And it is thanks to your effort and sacrifice in stopping the spread of this disease that the death rate is coming down and hospital admissions are coming down.”
There have been 219,183 confirmed coronavirus cases in the UK and 31,855 people have died, according to the Government’s latest figures.
Before his address on Sunday evening, the Prime Minister clashed with the leaders of Scotland, Wales and Northern Ireland over his new “stay alert” slogan.
Scottish First Minister Nicola Sturgeon warned the messaging could be “catastrophic”, as each of the devolved administrations said they would keep using the “stay home” slogan.