We also have the Socialist Party here, founded by people who were chucked out of Labour for being too left -wing (dunno how Corbyn escaped the attention, but SP stopped fielding their own canditates when Corbyn became leader of labour, and started backing labour instead) A minor party but the only
real Labour party we have, ATM.
We also have the Green Party
And we have another very minor party called the Monster Raving Loony Party founded by this guy:
I reckon you could do with all of those parties in the States