I’m not sure what benefits you will get because you work full time. I work 21 hours and get working tax credit which pays for nursery . It’s not much because they take wages into consideration
I have a small mortgage so my wages covers that
I don’t think you will qualify for housing benefit and renting is really expensive but there is no harm in asking.
Do you live near your parents? I don’t have any everything was one big struggle but I was able to stay in my husbands house as everything was In his name. He is not the father of my child but took us to court to chuck us out even though I paid bills and maintained home while he was whoring.and taking drugs.