Moving to London, work, university,

Good evening. I am a full-time student with type 1 diabetes who have settled status and who is planning to move to London because the most important part of my life is in London. At the moment I am looking for work in London, and would like to ask, is it possible to get a council house, flat in London in future? And if yes, how long will it take approximately to get any update about my application?