PJ Media

From what we can see, “the left” in the UK are the proponents of international socialism, while “the right” believe that Britons should be able to run their own socialism without outside interference.

That is a very coarse first approximation. A slightly less coarse approximation is that “the left” in the UK are proponents of socialism and multiculturalism, while “the right” are proponents of feudalism.
Both anti-capitalists, but qualitatively different: placing them on the American left/right axis is a gross over-simplification.