HELLOOO, I have been/am in this situation so I know exactly what it's like!
I was living with a mate and his parents, renting a room in their house and when I got pregnant they were like "well you can't have a baby here so you'll need to find somewhere else to live"...so like you, I got onto the council and they sent a man round to assess my situation and discuss my options.
Well he was a twat, he basically said that I needed to go on the housing register but I would only be in band 3 or 4 (band 5 being the lowest), because I was "in lodgings" and had my own room, DESPITE the fact that I would be getting kicked out eventually. He said I could bid on houses but I really wouldn't get anywhere. So then he said that my only other 2 options would be to claim housing benefit for a single room in a shared house, OR, when I get kicked out, come down to the council with all my things in bin bags and they would POSSIBLY put me in temp accomadation.
So a couple more months went by and the situation was still looking bleak. I even went as far as writing a letter to my local MP who didn't actually do anything to help me, but ironically it was his reply that led to me being put where I am today. At the end of his letter were phone numbers for people in the council if I wanted to discuss things with them. So I just picked up the phone one morning and said "hiya, I'm 6 months pregnant and I'm going to be made homeless on the 31st of this month". So she then asked me if I'd ever heard of Bartletts Parent and Child Project and then referred me for an interview with them. They basically home people like you and I who are in these kinds of situations and then when baby is born they send a thing to the council saying you've had your baby and the council then put you up to band 2 on the housing register and you bid on houses and then move into your own permanent place. The place I have moved into is lovely! It's a 2 bedroom house and it's just been renovated and the rent is £11 a week including bills
ANYWAY, this all depends on whether or not your council runs a scheme like this BUT if they don't, I know that all you need to do is tell them you are becoming homeless on whatever day (you really need to give them notice) and I think provide a letter from the people you are living with or your landlord stating that they are evicting you and they will then put you in temp accomadation. But don't worry seriously you won't be put in with a load of druggies!
Wishing you allt he luck in the world and if you need to chat just pm me

xxx