Despite a lot of interest, there’s only a small amount of co-op housing in the UK. Most non-profit housing is charitable housing associations. Large housebuilders have a stranglehold on the market overall.
“the Swiss example shows how these non-state and non-capitalist actors can build quality housing at a mass scale, if they’re encouraged — and that they can create a model of housing provision that moves beyond speculation into something more democratic and innovative.”
This article points to Switzerland and Zurich in particular as examples of more active housing co-op markets. Although it doesn’t give much insight into how to get to that point from our current position in the UK.