See here, for example:
Accounting for over 20% of the total housing stock, the sector is largest in Austria, Denmark, and the Netherlands. Finland, France, Iceland, Ireland, and the United Kingdom have a moderately-sized social rental housing sector (between 10 and 19% of the stock). By contrast, the sector is relatively small (between 2 and 10% of the total stock) in Australia, Belgium, Canada, Czechia, Germany, Hungary, Italy, Japan, Korea, New Zealand, Norway, Poland, Slovak Republic, Slovenia, Switzerland, and the United States. The social housing stock is smallest in Colombia, Estonia, Israel, Latvia, Lithuania, Portugal, and Spain, where it accounts for less than 2% of the total housing stock (data on the number of dwellings in absolute terms are available in the online Annex, PH4.2.A1). www.oecd.org/content/dam/oecd/en/data/datasets/affordable-housing-database/ph4-2-social-rental-housing-stock.pdf
No clear relationship at all between the % of social housing and the extent of housing crises (Israel, for example, has very affordable housing and a high fertility rate - and it's almost all done through the private sector).
Social housing per se is fine but you do need to actually build it, and it's not clear to me that the public sector in the UK has the money to start building tons of housing stock. It would be easier to reduce regulations/change the planning law, and make it easier for the private sector to build like mad.