The expenses incurred by a joint committee of two or more local authorities whether appointed or established under this Part of this Act or any other enactment shall be defrayed by those authorities in such proportions as they may agree or in case of disagreement as may be determined—
(a) in any case in which those authorities are the councils of parishes or groups of parishes situated in the same district, by the district council;
(aa) in any case in which those authorities are the councils of communities or groups of communities situated in the same principal area, by the council of that area; and
(b) in any other case, by a single arbitrator agreed on by the appointing authorities or, in default of agreement, appointed by the Secretary of State.