A work may be contemporary, and in copyright, but anonymous (=anon). This problem is one of the flavours of this year for copyright lawyers, who call such works "orphan works".

Originally (well, at least before the Copyright Act 1911 and in some respects before the previous Fine Arts Copyright Act) was a monopoly for publishers not composers, which was why IMHO if the first publisher of a work is known it is not "anon".

"Public Domain" is not a term of art in UK copyright law.

"Public Ownership" AFAIK has no meaning at all.

And a work may be IMHO "traditional" without being anon.

There are references to "folksongs" in the headings of S 61 and S 169, but the word is not used in the sections (ie the operative parts) and not defined.