Antiracist and leftist is kind of an exaggeration; rather an apolitical subculture of the British working class up until the late 70s/early 80s when the National Front infiltrated the scene. This was during the second wave of the skinhead movement, the original skinheads in the 60s were influenced by West Indian immigrants to the UK, and listened mainly to ska and jamaican music, but generally not very politically conscious or involved. Kind of a rougher offshoot of the mod subculture.

The second wave of skinheads came out of the punk movement. A lot of skins were into Oi!/streetpunk and the NF made their own version which was then called RAC (Rock against communism) but is better known these days (at least in Europe) as White Power Music.

I'm not saying there weren't leftist skinheads (Redskins and Angelic Upstarts would be a good place to start) but as a subculture, the common theme is rather working class identity and pride - which unfortunately, as we've seen, can be exploited by fascist movements as well.