So basically we've got

a) Traditional songs about actual (easily identifiable) kings and queens: not many of them, generally not anti-monarchist or scandalous (e.g. Queen Jane)

b) Traditional songs about more or less mythical kings and queens: tons of them, not anti-monarchist but often scandalous (King X and Queen Y shagging around, having people killed on a whim etc)

c) Traditional songs slagging off one king but saying that he should be replaced by another king: tons of them, sometimes scandalous, not anti-monarchist

d) Modern songs slagging off the monarchy in general: anti-monarchist, scandalous as you like, not traditional.

Quoting the OP:

I am looking for British songs and tunes from all ages which reflect ant-monarchist sentiments.

A: There aren't any from "all ages" - just from this age (more specifically, from the reign of the present queen).