I did a TL where this occurred in the 19th century.
It developed with the main parties and general policies:
Progressive: William Gladstone's liberals. Left wing. Favour social programmes but a liberal economy and a very active foreign policy. Get into power a lot as they're always the second choice of the extreme left and the economic liberals.
Labour: Socialists. Quite like OTL old labour really. A bit insular. Get power sometimes.
Liberals: Pseudo-ibertarians. Quite popular.
Conservatives: Quite like old school conservatives. Racism, classism, protectionalism. That sort of thing. Pretty much turn into the BNP. Start well but by the second half of the 20th century wither away.
And then there's also a bunch of smaller parties like the greens, the silvers (technology pushers), various national parties and local interest groups, Imperial Party (Tory splinter who are a bit nicer but minor), etc...
Just my take of course. Things would no doubt be different but it'd be interesting.