The local authorities for the purposes of the Public Libraries and Museums Act 1964 in England shall be county councils, . . ., London borough councils, district councils, the Common Council and the Council of the Isles of Scilly and, subject to the provisions of section 5 of that Act, each of the following authorities, that is to say—
(a) the council of a non-metropolitan county;
(b) the council of a London borough and the Common Council;
(c) the council of a metropolitan district;
shall be a library authority for those purposes.