Looking at the roots of the song it is fair to say it is most associated with the Labour Party. His memorial in Ireland talks about the 'anthem of the International Labour Movement'. Jim Connell wrote the song when he was a member of the Social Democratic Federation and the Labour Party did not exist.

Wikipedia entry on Red Flags talks about 'The red flag became a symbol of communism as a result of its use by the Paris Commune of 1871'. So clearly Jim Connell was taking inspiration from the Communists of Paris.

Not sure if this proves my point. Probably doesn't, but I must do some work rather than Socialist research.