> Another nugget in there is that something like 95-97 of the population has Covid antibodies
That is almost certainly wrong. Vaccine uptake in under-12 is 0% and vaccine uptake in young adults is low. There's no way to make those kinds of seroprevalence numbers work.
The PHE report measures both antibodies from natural immunity, and antibodies from (vaccine or natural infection or both). (They don't have a vaccine-only measure.) The former is in the 20% range, depending on age. The latter is in the 97%+ range, again depending on age, reaching essentially 100% for older people.
The big caveat is that the sample population consists of blood donors, which may or may not be representative of the overall population.
That is almost certainly wrong. Vaccine uptake in under-12 is 0% and vaccine uptake in young adults is low. There's no way to make those kinds of seroprevalence numbers work.