Around eight in 10 adults in most parts of the UK have COVID-19 antibodies, according to the Office for National Statistics (ONS).
An estimated 80.3% of adults in England now have signs of immunity from either a vaccine or having had the virus in the past, blood test results for the week beginning 17 May suggest.
This is up from seven in 10, or 69.9%, a month earlier.
In Wales, the figure is 82.7% in the same week - up from 66.8%; in Scotland it is 72.6%, which is up from 59.9%; and Northern Ireland's estimate is 79.9%, which is up from 68.8%.
The estimates are for people in private households and do not include settings such as hospitals and care homes.
It takes between two and three weeks after infection or vaccination for the body to make enough antibodies to fight the coronavirus.
They then remain in the blood at low levels, although these can decline over time to the point when tests can no longer detect them.
The ONS said there is a clear pattern between vaccination and testing positive for COVID-19 antibodies but the detection of antibodies alone is not a precise measure of the immunity protection given by vaccination.
Once infected or vaccinated, the length of time antibodies remain at detectable levels in the blood is not fully known.
It is also not yet known how having detectable antibodies, now or at some time in the past, affects the chance of catching the virus again.
The figures will give the government food for thought, as it prepares to make a decision on whether to go ahead with the final stage of easing lockdown in England on 21 June.
However, despite the optimistic data, the highest proportion of those testing positive for antibodies were people aged 60 and over - who are most likely to have been fully vaccinated.
In addition, vaccine hesitancy is still proving a problem in the most deprived areas of the UK.
More data from the ONS showed that hesitancy around taking the COVID-19 vaccine is around three times more likely for people living in less affluent parts of the country.
One in 10 people in those areas reported vaccine hesitancy between 28 April and 23 May, according to the statistics body, compared with 3% in the least deprived areas.
Across the UK, 94% of adults responded positively to the question of taking the vaccine - compared with the previous figure of 93%.
All the vaccines approved for use in the UK have met strict standards of safety, effectiveness and quality, and reports of side effects are "very rare", according to the NHS.