Don’t expect to be given a flat right away, especially with Southwark council.
They were voted as the worst council in London.
In regards to temp accommodation, you will likely be put in a room at first. You will have kitchen and wash facilities, they can only keep you in that room legally for 6 weeks whilst they do all they’re checks to see if they have a duty to house you.
After 6 weeks they must find you a suitable temporary place to live, in your case you will be entitled to a two bedroom as your son is over one, however these are in high demand so you’ll likely be given a one bed.
They can and will move you out of London if they cannot find a suitable property within the borough, which stretches from Crystal Palace down to Bermondsey so you can be placed anywhere inbetween. You cannot refuse these offers as they will then release you from their duty of care and deem you intentionally homeless.
You will then go onto the bidding system, if there are no medical conditions or special circumstances, you will go into band 3 and have to bid weekly for a two bed flat or house whichever is on there.
Band 3 has a 5-7 year wait list, they do not give out direct offers anymore so you have a very long wait ahead of you.
Whilst in temporary accommodation, the council must provide you with a fridge and a cooker everything else you need to provide for yourself.
They can also move you at anytime, especially if you are provided with a privately owned temporary accommodation.
Also when bidding make sure it is somewhere you really want to live as again you only get one chance of you refuse the offer they will close your case and you will then have to go private.