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That seems to be a different company (based in Bedfordshire), the one that Channel 4 were talking to are based in Belfast (I think, certainly NI). Also they are talking about developing a test, where the NI company seem to have one they are already shipping.
My understanding (and its minimal) is that the RT PCBs test for the actual virus, whereas the antibody tests test to see if you are producing the antibody to it. An amount of the antibody will continue to be produced and in your body forever once you have recovered. Thus the antibody tests can check if you have had it, if they are sensitive enough.
But I may have misunderstood something in there.
This gives more information on your second link: https://mologic.co.uk/mologic-awarded-c-1-million-by-uk-government-to-develop-rapid-diagnostic-test-for-covid-19/
I can't find any information on whether it can test for those who have had it and recovered, rather than just those who are currently infected.