I can help as I've just been through this. The outcome from the council completely depends on the reason for you being evicted.
firstly you get the notice to quit which is normaly 2 months notice, that is basically just ending your tenancy, then the landlord has to apply for a possession order (it took 5 months from when I first received my notice to quit) you will get papers for the court that you have to fill in regarding the possession order, that normally takes around a month to go through and you will usually have 2 weeks until the possession order takes effect, but you
don't have to leave when that takes effect, they then have to apply for a balliff order which take another month roughly and it will give you a date and time depending on how busy the balliffs are when they will come and repossess the property and change the locks and you
have to leave or be gone by then
As to the council once you receive your possession order they will doing a housing assessment with you to decide whether you are intentionally homeless or not, if you are considered intentionally homeless they will only provide temporary accommodation for 28 days to give you extra time to look for a private rental, if you are
not considered intentionally homeless they will offer you temporary accommodation until you get a permanent council house HTH