Antibody rates are now more than 50 per cent higher than epidemiologists predicted they would be when they published models which informed the Covid roadmap.
In February, Imperial College warned that only 44.6 per cent of the population would be protected by the original release day of June 21.
But the latest figures from the Office for National Statistics (ONS) show that eight in 10 people over the age of 16 now have antibodies to Covid.
For the whole population, including children, nearly seven in 10 have immunity – 54 per cent higher than the modellers predicted.
The percentage of those with immunity is likely to be higher still because many under-16s will have had a previous infection and the data only runs up to June 7, meaning it does not include vaccinations and infections in the last fortnight.
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The new figures also show that nine in 10 over-34s have antibodies to the virus, while more than 99 per cent of the over-65 have measurable immunity.
Even among the lowest age groups, the figures are creeping up as younger people get vaccinated.
Sarah Crofts, the head of analytical outputs for the Covid-19 infection survey, said: "Across the UK at least 80 per cent of adults now have some level of antibody protection against Covid-19.
"With infection levels now increasing again in England, this protection will hopefully protect the majority against severe symptoms. With vaccinations now open to the under-30s, we must continue to monitor how antibody levels change over the coming months.”
The ONS said more people may have immunity, but at lower levels than can be picked up by testing or through other parts of the immune system such as T-cells.
Paul Hunter, a professor in medicine at the University of East Anglia, said: "The most obvious findings are that in all the age groups over 34 for England the modelled percentage of people with antibodies is over 90 per cent and in the 60 to 79 age groups it is over 95 per cent.
"This is a remarkably high rate and most of this will be due to the impact of vaccines. What is perhaps even more reassuring is that the rate of people aged 25 to 34 is 69 per cent, and aged 16 to 24 is 56 per cent.
"The presence of antibodies is strongly correlated with at least some degree of protection. So this is very good news, even for younger age groups in that a substantial proportion – probably even the majority – of those younger age groups already have some degree of protection.”