Video report by ITV News Correspodent Romilly Weeks
As set out in the PM's roadmap out of lockdown, adjustments to restrictions will see hospitality venues reopen for indoor service and international travel restart for some destinations.
Other expected changes include the resumption of indoor entertainment, such as theatres, and sports stadia will be allowed to accommodate fans at large events.
While millions have been expecting many of the relaxations, the changes announced to social distancing and universities may have come as more of a surprise.
From May 17 people will have the choice on whether to socially distance from friends and family, meaning hugging will once again be permitted.
The government urged caution, reminding that some people are "more vulnerable" to severe illness from Covid-19 adding that while vaccines reduce the risk, they do not eliminate it entirely.
Wider social distancing rules will remain in place in adult social care, medical, retail, hospitality and business settings.
Another surprise is the return to the classroom for all university students, who will be able to enjoy in-person learning for the first time in months.
The prime minister said "good progress" had been made in the past month, with infection rates at their "lowest level since last September, and deaths and hospitalisations are at their lowest level since last July".
He said the "four tests" had been passed, meaning vaccine deployment is continuing successfully, jabs are reducing hospitalisations and deaths, infection rates are not at risk of surging, and assessments have not changed due to new variants.
ITV News Science Editor Tom Clarke discusses the science around Covid and hugging
Mr Johnson said the UK had vaccinated more than two-thirds of its adult population, with more than 17 million people having received their second dose.
He said England remains "on track" to end all legal restrictions on June 21, after thanking the public for efforts fighting the virus which have "so visibly paid off".
He said he'll provide an update later this month on what, "if any" role social distancing and coronavirus health certificates would play after June 21.
Despite positive news about the UK's battle with coronavirus, England's Chief Medical Officer, joining the PM at the press conference, said he's concerned about cases of the Indian variant of coronavirus which have been found in the UK.
He said most foreign variants are "relatively stable and not increasing at a great rate", but the Indian variant - also known as B1.617.2 - is "slightly concerning in terms of increasing as a proportion".
He added: "This is actually spreading from very small amounts but it is beginning to spread in certain parts of the country and we need to keep quite a close eye on this."
Mr Johnson said he was resisting pressure to bring forward any lifting of restrictions, regardless of positive data.
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He said next Monday's easing is "a very considerable unlocking" which will bring "a lot of extra movement, a lot of extra contact".
"We think it's prudent, we think we can do it, but it's got to be done in a way that's cautious and I think that we will want to have time to see the effects," he added.
The PM's lockdown announcement follows an agreement between the four UK chief medical officers that the Covid-19 alert level should move from level 4 to level 3.
A statement said: “Thanks to the efforts of the UK public in social distancing and the impact we are starting to see from the vaccination programme, case numbers, deaths and Covid hospital pressures have fallen consistently.
“However Covid is still circulating with people catching and spreading the virus every day so we all need to continue to be vigilant. This remains a major pandemic globally.
“It is very important that we all continue to follow the guidance closely and everyone gets both doses of the vaccine when they are offered it.”
Here are the main things that will change in England from May 17:
People will be able to meet outdoors in groups of up to 30 people, and meet indoors in groups of up to six or as two households
The majority of sectors will reopen, including pubs, bars and restaurants indoors
Indoor entertainment will resume, including cinemas, museums and children’s play areas
Theatres, concert halls, conference centres and sports stadia can all re-open, with larger events in these settings able to resume with capacity limits
Organised adult sport and exercise classes can resume indoors and saunas and steam rooms may reopen
All remaining accommodation including hotels, hostels and B&Bs can re-open
Domestic overnight stays will be allowed in groups of up to 6 people or two households
Weddings, receptions and other life events can take place with up to 30 people
Cap to be lifted on numbers attending funerals, in line with how many people can be safely accommodated in venues
Up to 30 people will be able to attend a support group or parent and child group. The limit does not include children under 5
Care home visiting will be eased, with residents able to have up to five named visitors and greater freedoms to make low risk visits out of the home
Face coverings for pupils will no longer be recommended in classrooms or in communal areas in secondary schools and colleges
All remaining university students will be eligible to return to in-person teaching and learning and should get tested twice a week upon return
Social distancing between friends and family to become a choice, meaning hugging will be allowed
Social distancing rules to remain in place in adult social care, medical, retail, hospitality and business settings
The ban on international travel will lift and be replaced by a traffic light system
Watch the press conference in full: