Why?
For reference, I think this system is safe, but don't understand your point here. The government and the NHS are different institutions with different motivations.
In Germany, there is an enormous amount of paranoia about collected data, owing to the historical legacy of Nazi rule. The tax office, the government, the housing authorities, the benefits office, the police... all on different systems that never intersect. From a basic admin perspective, it can be absolutely torturous. Saying that, realising quite how interconnected the UK is compared to other developed European countries can be eye-opening...
I think in an age in which data is so intertwined with our own entertainment, media and identities, it is reasonable to apply at least some caution to our collective rights in this regard. An increasing majority of people seem to notice patterns in their targeted advertising that leave them convinced that their iPhones and other devices are listening in on their communications. I'm personally not convinced, but what's more unnerving is the amount of citizens who relate to the thrill of this conspiracy but also seem completely adjusted to the idea?