It applies to any Constable.
You don’t have to carry your FAC but if you fail to produce it when requested while in possession of firearms they can be seized:
2)If a person upon whom a demand is made under this section fails to produce the certificate [
F2or document] or to permit the constable to read it, or to show that he is entitled by virtue of this Act to have the firearm, ammunition or shot gun in his possession without holding a certificate, the constable may seize and detain the firearm, ammunition or shot gun and may require the person to declare to him immediately his name and address.
Have a read of the relevant sections of the 1968 Act and in particular
Section 48