Registration is a JAA requirement and therefore does not apply in any way to a non JAA licence e.g. an NPPL.
There is no requirement in the ANO so it is not law. As Billiebob says a Flying Club is whatever you want it to be; two persons with a common interest will do nicely.
The ANO Art 126 does require a licensed aerodrome for instruction for the issue of a licence however; there are Exemptions to allow license training on
Microlights and
SLMGs from unlicensed aerodromes.
A FI can teach for an NPPL at a licensed aerodrome; subject to the privileges of his/her licence and rating, and at unlicensed aerodromes in accordance with the above Exemptions.