Political or not, a song should be well-crafted with knowledgeable writers doing the service.
Whether it's a Left-wing song or a political song is irrelevant. The question to be asked is
"Is it a good song" with imagery, context, a sense of form, appeal to the senses and not generalizing, stanzaic consistency (either uniform or not), subject matter that reach people,
and not inane preaching but "showing".

Eric Bogle, Stan Rogers, Woody Guthrie, Leadbelly, Pete Seeger, Tom Paxton, Tom Lehrer and occasionally a song crafted for a rally or demonstration can be useful (though probably not for a concert).

There must be plenty of good songwriters in the UK who I don't know about.

I found Rosselson to be a little too glib and clever (without being clever like Tom Lehrer).

Peggy's songs "Engineer" and a couple of others are very good especially when she doesn't feel obliged to "screech" her message with a shrill voice. The lady can sing and write.

Don't forget Jean Ritchie, "Black Waters", "The L. and N. Don't Stop Here Anymore".
These are terrific songs and have a political intent.

Expressing political intent in a song is fine as long as it's a good song (see definition above).

I think it's perfectly fine and important to rewrite lyrics to traditional songs to reflect contemporary times provided that there is an understanding of the source material.