Take into account that the NHSX approach is most accurately described as partially centralised. A real centralised approach is what the Chinese and the Koreans

Take into account that the NHSX approach is most accurately described as partially centralised. A real centralised approach is what the Chinese and the Koreans have where phones are constantly recording and transmitting location data. The NHSX and Google/Apple approaches both restrict what data they record, they just made different judgements about what privacy tradeoffs were reasonable in order to deliver contact tracing and alerting. So it's not the case that privacy was never considered by NHSX, just that they wanted to do things that you cannot do without some degree of centralisation. Most importantly they warn you when a contact develops symptoms and then warn you again if they test positive. That would help get at least some people reducing their contacts earlier. Apparently despite some very clever design on their Bluetooth system they never got it to work well enough.