People attending nightclubs and other venues where large crowds gather in England will need to be fully vaccinated from the end of September, the government says.
Latest figures show 35% of 18 to 30-year-olds have not had their first jab.
Currently nightclubs and other crowded venues are only encouraged to ask clubbers to show proof of vaccination, a negative test result or immunity.
But Boris Johnson said he was concerned by the continuing risk of transmission.
The announcement came on the day nightclubs in England were allowed to reopen after 16 months of closure.
The prime minister told a press conference on Monday: "I don't want to have to close nightclubs again as they have elsewhere. But it does mean nightclubs need to do the socially responsible thing.
"As we said last week, we do reserve the right to mandate certification at any point if it's necessary to reduce transmission.
"And I should serve notice now that by the end of September, when all over 18s have had their chance to be double jabbed we're planning to make full vaccination the condition of entry to nightclubs and other venues where large crowds gather."
Chief scientific adviser Sir Patrick Vallance said nightclubs and other such venues could be "potential super spreading events" because of crowds in close contact.
"I would expect that with opening of nightclubs, we'll continue to see an increase in cases, and we will see outbreaks related to specific nightclubs as well," he said.
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Nightclubs are still closed in Scotland, Wales and Northern Ireland.
The Welsh government said it would never mandate the use of vaccination certificates but that businesses would be free to ask for them.
Across the UK, 39,950 cases were recorded on Monday alongside another 19 deaths within 28 days of a positive test.
It's easy to understand how a loud and busy nightclub could be the perfect stomping ground for Covid.
Having lots of people packed closely together, snogging, singing and shouting in a confined space with relatively poor ventilation creates ideal conditions for a virus carried in our spit to spread.
Add in the fact that many of those attending may not have had two or even one dose of a vaccine that helps protect against catching and transmitting the virus, and you could have a super-spreading event on your hands.
The Netherlands recently tried reopening its clubs and quickly decided to close them again amid rising infection rates. Its government said most of the new infections occurred in nightlife settings and parties with large numbers of people.
For now, it is asking its citizens to use their common sense and act responsibly; keeping gatherings small and manageable. Time will tell if the UK might go the same way.
Many nightclubs have shut down during the pandemic and the industry reacted angrily to the prime minister's announcement.
"So, 'freedom day' for nightclubs lasted around 17 hours then," said Michael Kill, boss of the Night Time Industries Association.
"Leaving aside the fact that this is yet another chaotic U-turn that will leave nightclubs who have been planning for reopening for months having to make more changes to the way they operate - this is still a bad idea.
"80% of nightclubs have said they do not want to implement Covid passports, worrying about difficulties with enforcing the system and a reduction in spontaneous consumers, as well as being put at a competitive disadvantage with pubs and bars that aren't subject to the same restrictions and yet provide similar environments."
Boss of UK Hospitality Kate Nicholls called the announcement "a hammer blow" for a struggling industry trying to rebuild.
One major nightclub firm, Rekom UK, which owns 42 venues including chains Pryzm, Bar&Beyond, and Fiction, said clubs had become a political football.
Boss Peter Marks said: "Mandatory Covid passports may make sense one day once the entire adult population has been offered vaccines, but does government really think this threat will entice the 'vaccine wary' to take the vaccine? They will just stay later in the pubs and hold their parties in their houses."
Mark Harper MP, who chairs the Covid Recovery Group of Conservative backbenchers, also criticised the plans, saying the government was "effectively moving to compulsory vaccination."
Speaking in the House of Commons, he called on the government to bring forward the evidence for the policy in September ahead of any vote, saying he didn't think the evidence from pilot schemes supported the idea.
Vaccines minister Nadhim Zahawi MP promised to share the evidence with the Commons, "working with the nightclub industry or at-risk large scale events that are indoors".