The presence of Covid-19 antibodies implies someone has either had the infection in the past or has been vaccinated, and it takes between two and three weeks after infection or vaccination for the body to make enough antibodies to fight the virus.
Antibodies then remain in the blood at low levels, though these levels can decline over time to the point where tests can no longer detect them.
It is also not yet known how having detectable antibodies, now or at some time in the past, affects the chance of getting Covid-19 again.
The latest ONS estimates were based on a sample of blood test results for the week beginning 19 April.
They reflect the ongoing impact of the vaccine rollout across the UK, in particular the increasing number of people who have received both doses and are now fully vaccinated.
Government figures show that by 19 April, 33,032,120 first doses of vaccine had been given - the equivalent of 62.7 per cent of adults - along with 10,425,790 second doses (19.8 per cent adults).
The ONS said across all four nations 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.
The ONS estimates are for people in private households and do not include settings such as hospitals and care homes.
In England, the highest percentage of adults testing positive for Covid-19 antibodies in the week beginning 19 April was estimated to be the 80 and over age group (92.3 per cent), followed by people aged 75 to 79 (88.8 per cent) and 70 to 74 (86.4 per cent).
The lowest percentage was for 25 to 34-year-olds (46.2 per cent).
In Wales, the highest proportion of adults likely to have tested positive for antibodies was the 80 and over age group (90.4 per cent) followed by 75 to 79 (87.0 per cent), while in Scotland the highest percentage was for people 80 and over (88.2 per cent) followed by 65 to 69-year-olds (82.4 per cent).
In Northern Ireland, the ONS uses different age groups due to small sample sizes and estimates 83.4 per cent of people aged 70 and over were likely to have tested positive for antibodies in the week beginning 19 April.