But the prime minister said he was “confident” that the date of so-called Freedom Day - initially scheduled for 21 June - will not have to be postponed again.
And he said that scientists were not advising the reversal of any of the relaxation of curbs in areas like shopping and hospitality introduced over the past few months.
With Downing Street seeing the coming weeks as a race against the virus and the vaccine, the target for offering a first jab to all adults in England is being brought forward from the end of July to 19 July.
And the delay between first and second jabs is being cut from 12 to eight weeks for over-40s, as scientists said promoting high vaccine uptake is critical to suppressing the worst effects of the third wave.
The authorities believe that by stepping up inoculations, around two-thirds of adults will have been offered a second dose by 19 July, significantly reducing the risk of hospitalisation and cutting deaths by thousands.
Mr Johnson said: “It’s unmistakably clear the vaccines are working and the sheer scale of the vaccine roll-out has made our position incomparably better than in previous waves.
“But now is the time to ease off the accelerator because by being cautious now, we have the chance in the next four weeks to save many thousands of lives by vaccinating millions more people.”
He said that the extra four weeks would give medics time to build a “very considerable wall of immunity” around the whole of the population by maximising vaccinations.
But he admitted that he could not rule out the possibility that the emergence of new and even more virulent variants may force a further delay in the return to more normal life.
A two-week review will be carried out on 28 June, but Downing Street made clear it was thought unlikely that the situation will have improved enough by then to allow reopening to be brought forward to 5 July. The result of a second review, announced on 12 July, is expected to lead to the lifting of remaining restrictions a week later.
The PM held out some consolation to couples planning to get married or enter civil partnerships over the coming weeks, announcing that the cap of 30 attending ceremonies and receptions is to be lifted.
Care home residents will no longer have to self-isolate for 14 days after trips outside the premises. And trials of mass attendance events with audiences of various sizes will continue, meaning there is no change to numbers of fans expected to be allowed to attend Euro 2020 football matches.
But he said there would be no additional financial support for businesses hit by extended closure, despite warnings that the delay will cost the nightlife and hospitality sector alone as much as £3bn. The moratorium on commercial evictions will end as scheduled on 1 July, despite many businesses now not being able to reopen until after that date.
The UK is now recording around 8,000 positive Covid cases a day, the highest level since February. Numbers are growing by 70 per cent nationally week-on-week and are doubling weekly in areas with higher levels of infection, focused in the northwest of England but now covering one-third of the country.
Average numbers of people admitted to hospital are increasing by 15 per cent each week - but by 66 per cent in the northwest. But deaths remain low, with just three recorded nationwide on Monday.
Mr Johnson told a Downing Street press conference that the spread of the Delta variant meant “we have obviously faced a very difficult choice”.
“We can simply keep going with all of Step 4 on 21 June, even though there is a real possibility that the virus will outrun the vaccines and that thousands more deaths would ensue which could otherwise have been avoided,” he said.
“Or else we can give the NHS a few more crucial weeks to get those remaining jabs into the arms of those who need them.
“And since today I cannot say that that we have met all our four tests for proceeding with Step 4 on 21 June, I think it is sensible to wait just a little longer.”
A bride-to-be who has had to postpone her wedding twice asked the prime minister why testing and vaccination status cannot be used to open up weddings in the same way it is being used for football matches.
Speaking to the Downing Street press conference by video link, she said it felt like weddings are “bottom of the priority list despite being significant life events without which some people cannot progress with their lives”.
Mr Johnson said he was “very, very sorry” to hear about her situation, adding: “All I can say is I’m sorry for the disappointment that this will certainly bring to weddings, to many, many businesses, but it’s a few weeks that I think is worth it to get those jabs in.”
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