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Test always perform worse than hoped when used in real world situations. What's key here is that the antibody tests used pre-COVID blood as a negative control. They were designed to say anyone with prior immunity was 'negative'. They tell us who had COVID not who is immune now. https://twitter.com/deeksj/status/1326786353254854658
There's always a grey area between definite positives and definite negatives. If you include all the grey area you find that over 40% of the population are had immunity to COVID in May. https://www.medrxiv.org/content/10.1101/2020.08.20.20178533v1.full.pdf https://www.medrxiv.org/content/10.1101/2020.06.08.20120584v1
But PHE went one step further. Instead of testing for just the unique spike protein antibodies they tested for all the COVID proteins. They found more than half of people who had no symptoms in spring (ie were immune) had antibodies. https://www.thelancet.com/journals/eclinm/article/PIIS2589-5370(20)30341-2/fulltext
Add that to the 7% who had COVID and we are at herd immunity.
Only 3% of Wuhan hospital workers had antibodies on specific testing (like the ones used by government for population testing). This does not mean only 3% of Wuhan hospital staff are immune. https://www.nature.com/articles/s41591-020-0949-6
There's plenty of other evidence that backs this up: Maximum household transmission only 50%; T-cell immunity prior to COVID 50%; Gompertz curves all bending at same point regardless of intervention; lack of COVID in areas that had SARS1.
