The technical answer seems to be that the relevant legislation (Representation of the People Regs 2001) only provides for an electoral register being provided to the local council, on request. It does not make any provision for a parish meeting where there is no local council.
I can only speculate on the reasons for this. Use of electoral registers is highly restricted, for the protection of citizens. It may be that the legal position of a parish meeting, being looser than that of a local council, means that it is thought to be more difficult to impose restrictions.