You raise an interesting point, I used to believe mandatory cards would be an imposition of the state, i.e. the state is answerable to the people, not the other way round.
However, for a host of reasons, including illegal immigration and fraudulent misrepresentation. I think it's time to make them mandatory.
You would be expected to be able to prove who you are more often, for example you're selling a car, or involved in an accident, evading a train fare etc.
Currently we have a pantomime of people lying and evading justice, by saying "I don't have any id on me".
I still see it as an imposition, but an acceptable one.
Implementation would be key, and a technical, political and social minefield, which is why it's likely to be avoided as long as possible.
(Tangent Warning!)
Not sure about your reference to the Post office, Horizon was originally developed by ICL (Established by the Labour government in 1968), which was later bought in 1998 by the Japanese company Fujitsu, which had been listed on the UK stock exchange in 1981) More here!