To be honest, they feel more New Labour than actually left, to me. And New Labour was basically Tory-lite. The SMC comes from that sort of icky looks-left-but-acts-right ideology. It's all neo-liberalism (do as thou wilt so long as you're powerful), calls to listen to and obey authority 'because', and highly corrupt nepotism/cronyism.
The Socialist Workers Party and disability charities tend to be the ones I see protesting here. They're on the left. The BPSers claim to be on the left, but they're that smug sort of bourgeois liberal that thinks they're cleverer than everyone else, but deceives themselves into ignoring their own oppressive behaviour.