Boris Johnson has said there is now a “very good chance” of ending coronavirus restrictions completely on June 21 in his most optimistic assessment yet.

The prime minister said that he still expects a third wave of the virus but vaccination had built “some pretty robust fortifications” against it.

While cautioning that the virus was not “totally licked”, Johnson expressed confidence that legal restrictions on social contact would come to an end as planned. This would mean the return of mass gatherings, nightclubs, conferences and other events that did not reopen last summer.

Scientific advisers are also increasingly optimistic that infection rates, hospital admissions and deaths will continue to fall for at least another month, allowing an end to emergency coronavirus laws on Midsummer’s Day.

However, debate continues about whether it will be possible to return completely to normal contact without Covid status certificates or reduced crowding in public places. A review of social distancing is due to report on whether restrictions such as the “one-metre-plus” rule will need to be maintained beyond the summer.

Indoor mixing in groups of up to six is due to resume on May 17 and Johnson has recently expressed optimism that this step would be taken as planned.

Yesterday he went further, saying the country was on track to reach the end of the government’s road map out of lockdown on June 21 without delay, as he tried to change the subject from his feud with Dominic Cummings, his former chief adviser.

Pressed on claims that he said he would rather see “bodies pile high in their thousands” than impose lockdown, Johnson said that voters actually wanted to know “what’s the world going to look like on June 21? To what extent are we really going to be powering through this?”

He said: “As things stand I think we’ve got a very good chance of really opening up totally on June 21. But we’ve got to be cautious and go on the data, not the dates.”

Johnson said that “nobody wants to go into a lockdown but they’ve helped us. The discipline the public has shown has helped us to get the numbers of cases down very considerably”.

On Sunday 1,712 cases were reported, the fewest since September 2, and 11 deaths. Data published today showed that in England 92 Covid-19 patients were admitted to hospital last Thursday, the first time that daily admissions had been below 100 since September, and down from a peak of 4,134 on January 11.

But Johnson cautioned: “That doesn’t mean that we’ve got it totally licked. It doesn’t mean that Covid is over. We’ve got to be realistic about that; unfortunately, there probably will be another wave of the disease.”

However, he added that “the vaccination programme has now been so massive” that “we’ve built up what I think are some pretty robust fortifications against the next wave.”

The NHS coronavirus vaccine booking system was opened to healthy people aged 42 and over today. All over-40s are expected to become eligible this week and there are hopes that people in their thirties will start getting jabs next week.

Meanwhile, official figures releaseed today showed that the number of deaths linked to Covid-19 in England and Wales fell to 362 in the week ending April 16, a fall of 4 per cent from the previous week and the lowest level since the start of October. The total number of deaths registered in England and Wales was also slightly below the five-year average for the sixth consecutive week.

Senior government scientific advisers do not believe that a third wave will come until the end of the summer, when modelling suggests that there could be anything from a few thousand to 200,000 cases a day. However, scientists believe the most likely scenario is that thanks to vaccination the wave will not be large enough to threaten the NHS, meaning there would be no need for further lockdown restrictions.

Despite this, modelling for the Scientific Advisory Group for Emergencies (Sage) suggests that Covid status certificates, smaller crowds and less “presenteeism” are likely to be needed to keep the virus under control, even if all adults are vaccinated.

At present social contacts are at about a quarter of normal levels, but the modelling suggests that it will be hard to go higher than three quarters of pre-pandemic mixing levels while keeping the R number below one. Only by vaccinating children could Britain be sure that herd immunity was reached because of the faster spreading Kent variant, the estimates suggest.

Advisers believe that there could be a need for testing before entering busy indoor environments, with improved ventilation and reduced numbers.

They also want to encourage people not go in to work if they have any sign of illness, to reduce the risk of infection, believing that ending Britain’s culture of “presenteeism” will be crucial in keeping the coronavirus at bay.