If you think Switzerland doesn't have lots of factions, I don't think you've spent a lot of time in Switzerland.

I lived there for several years and I know exactly what you are talking about. There are a billion parties (or it seems like it) while the UK tends to have more factions grouped within larger parties. That said, as an outsider, I always saw this playing out a little differently in terms of national cohesion. Die Zauberformel tends to enforce that by design.