When can I consider "authorities" as a plural noun that has no singular form?

Most of the time it is found in the plural. From OALD, 4.

[countable, usually plural] the people or an organization who have the power to make decisions or who have a particular area of responsibility in a country or region I have to report this to the authorities. The health authorities are investigating the problem.

Rarely enough, this word is used in the singular with the same meaning, as for instance in "local authority" (Britain).

the organization that is responsible for the government of an area in the UK

Once the term has been introduced in a text there is the possibility to do away with the adjective and to write merely "the authority", although you don't have to; apparently, even when two occurrences of the term are found in close proximity the adjective is almost always retained.

(ref. 1) During the 42-day consultation period the local authority will serve a notice on adjoining owners or occupiers. The neighbour has a 21-day period in which to raise an objection with the local authority. The authority will take this objection into

(ref. 2) When such works are ongoing the local authority can prohibit or restrict the movement of mobile homes on to the site . The authority may attach a condition to the licence so as to require the completion of the necessary work

(ref. 3) Part 4 - Community protection Chapter 1 Community protection notices ( a ) the local authority that issued the community protection notice ; ( b ) if the community protection notice was not issued by a local authority , the local authority ( or , as the case may be, one of the local authorities...

The singular will be found also in other compounds such as the following.

the Highway Authority