Section 33A. Except as otherwise provided in this section and notwithstanding any other provision of general or special law, the service of all persons employed by every city in which this section has been accepted in the manner provided in earlier provisions thereof, or shall be accepted, in the case of cities having a Plan E charter, by the affirmative vote of two thirds of all the members of the city council, and, in the case of other cities by vote of the city council, subject to the provisions of the charter, and in every town in which it has been or shall be accepted by vote of the town at an annual town meeting, shall be restricted to five days and forty hours in any one week; provided, that, in cases of emergency, when the mayor or a city official designated by him, the city manager in cities having a Plan E charter, or a city official designated by him, and the board of selectmen or a town official designated by them, determines that public necessity so requires, which determination shall be final and conclusive, service in excess of the days and hours aforesaid may be authorized by an officer of such city or town or by any other person whose duty it is to employ, direct or control such employees, and such additional service shall be compensated for as overtime. This section shall not apply to policemen, firemen, school teachers, incumbents of offices specifically established by or under the authority of any general law or special act, or such other classes or groups of employees as from time to time may be specifically exempted therefrom in the manner provided for the acceptance of this section. The compensation payable to any employee shall not be reduced by reason of acceptance of this section.