If you apply for council/housing association you're put into bands in the waiting list. The bands depend on how in need you are e.g. homeless, disabled and in need of a more accessible property, need to move from your current housing and can't afford private. If you're homeless they will put you in emergency accomodation e.g. b&b, mother and baby unit, then you'll be top priority and be moved once a suitable place becomes available, but obviously you'll still be behind those in the same situation who have waited longer. You're definitely not just offered a council property when you have kids. I left an abusive relationship with my 6 month old and was staying in my friend's 1 bedroom flat with her and my baby but I wasn't considered homeless, and if I had claimed as homeless they would've involved social services to ensure my baby wasn't sleeping on the streets until they could've housed me. It's really not as simple and peachy as everybody makes out and you certainly don't have lots of help and benefits thrown at you just becaus you have children!
Edit.. if you have spare rooms in a council house you have to pay bedroom tax. Their rules are baby shares parents room until 1 or 2, after that they can share with opposite sex siblings until 10, and same sex siblings until 16. So e.g. a family of 2 adults, twin infants and 2 older sons could in theory be housed in a 2 bedroom flat.