OK, I agree that they, or myself, could be confused about antibodies or antigens.

Both my colleagues have completed their quarantine and been pronounced safe to return to work having been told that a second test is un-necessary as it would still give a positive result (and 90 day immunity).

My confusion is that thousands of new cases are being found every day.  I wonder how many of them are in fact people who have had the virus within the last three months, got over it without ever knowing that they had it, but are still giving a positive test result, after being tested for the first-time.

Neither of my colleagues knew they had the virus until family members tested positive and they then had a test.  Neither went on to develop any symptoms that would have alerted them to the fact that they had the virus.  One did have an intermitent head-ache for a couple of days but working in IT wouldn't have connected that to having Covid.

The fact that hospital admissions are rising might not be so much to do with rising case numbers, if that is the case as those that have had it are no longer capable of spreading the infection.  But because the more easily transmitted variant is simply infecting more people who are liable to need hospital treatment.