The UK's big parties are themselves a collection of factions held together by the inevitability of a two-party system. The ERG and Momentum are the most obvious

The UK's big parties are themselves a collection of factions held together by the inevitability of a two-party system. The ERG and Momentum are the most obvious, each pushing an agenda that, regardless of how much one agrees with it, has been incredibly divisive over the years: hard brexit and 'corbynism' (to avoid connotations of the 'S' word). These have been big gambles by the major parties, the details and direction of which have mostly been dictated by marketing and in-fighting. Despite having multiple general elections with these as the main issues, the public has only been presented with coarse yes/no choices and false dichotomies. In a multi-party system (e.g. proportional like STV) I'm pretty sure we'd see ERG as a separate party to Cameron-esque Tories, and Momentum as a separate party to the NewLabour/Starmer side of Labour. I'm not sure who would get the keep the old Labour/Tory names, though.