London is not representative of the entire country.
This.
We applied for council housing. Our council offers choice based lettings where they advertise the available properties each week and you register your interest against (up to) three. At the end of the week they look at each property to see who is first in line for it. The line is based on priority. When you apply for housing you get awarded Band P (absolutely priority, typically people who are homeless), Band 1 (urgent need for rehousing but not immediate such as current home over/under occupied or unsuitable for various reasons), Band 2 (need for rehousing but non-urgent such as someone moving for work or to give/receive support from family), Band 3 (no need for rehousing other than tenant preference, for example someone wanting to change areas). If two people of the same banding register an interest on a property then it goes on who has been on the housing register the longest.
We joined the housing register as Band 1 applicants, didn't bid for agesas there were no properties we liked the look of, then bid on three in one week and were offered one of them. Total time from joining the list to moving our stuff in was three months and this was in a popular area that previously had very few vacancies. Recently there are lots of vacancies in this area as the elderly tenants are dying/moving to sheltered accommodation/bungalows/in with family and it's freeing up the 2/3/4 bedroom homes. Before we moved to this street there hadn't been a vacancy in over ten years but in the last six months there have been four, all due to older residents moving on.
There are properties on the council list here advertised as "always available", you can have the keys in your hand the very next day regardless of your priority status. Those ones aren't in very desirable areas but the point stands that not everywhere in the country has years long waiting lists.
Councils need to invest in one and two bed properties for those downsizing and in bungalows for elderly people. They should offer once gives to people to downsize rather than forcing them. New build estates here have a certain percentage of the houses given over to Social Housing as a condition of the land sale and it seems a good model to follow. Developers get their land to build on, councils get new housing stock, everybody wins.
Oh, and our tenancy is a lifetime tenancy or Secure Tenancy as it's termed in our tenant pack. Secure Tenancy basically gives us certain rights and freedoms but it doesn't mean we're guaranteed this property forever. The tenancy moves from property to property so it isn't linked to one specific house, if we were to move from here to a smaller council property (e.g., when our DC leave home) then our Secure status would move with us along with all of our attendant rights and freedoms rather than us starting over as Probationary Tenants.