It might vary across the country for the exact particulars, but where I am if you somehow manage to meet the eligibility to get on the housing waiting list (very strict criteria for this), then weekly you get to bid on available properties that are available through the council to rent. How high you finish in the bidding depends on a score they give you (but you don’t get to see) which is calculated based on your ‘band’ of priority (for example I am band C for ‘lacking one bedroom’), the date you got put on the list, and other factors like medical need awards.
I’ve been on the list for four years now but getting nowhere near the top even still and with medical evidence bumping up my score a bit :(. Council housing is my only option to move out of my mum’s (where I moved with R when he was tiny and we escaped his dad) because I’m unemployed/unable to work and can’t afford private rents as they way outstrip what I’d get in housing benefit.
Tl;dr social housing in this country is severely fucked and there is only a fraction of the supply there should be because torys.