I am also looking for private rental but whats to happen if i dont find anywhere in 3 weeks when the new tenants want to move in!

Hi, i really need advice, i am 6 months pregnant and my tenancy run out the end of march(2 months ago) and my landlady asked if we wanted to renew, to which we said no as our place is very small and there wouldnt be room for a baby so we have given her notice that we was leaving. We found a bigger place to move to and the tenant there was being evicted we had a date to move in which is last month(may) but now the council have advised the tenant not to move and to squat in the property until they get a possession order which from what i have heard is going to take a long time. So this leaves me in a dilemma as i now need to leave where i am as new tenants are to be moving in at the end of this month(june), if i go to the council they will more than likely tell me to squat here which i am not prepared to do as I am on good terms with the landlady and she has been very good to me and i also know the new tenants that are moving into my place and dont want to hold things up for them, i have been told(though not sure if correct) that if i leave this place i will be making myself voluntarily homeless and the council wont house me. This whole situation has caused me lots of stress and worry and have had to see the doctor and he has said its anxiety. Sooo please any advice i would be most grateful!!! Thanks