I think you have been given the wrong information by housing. Council's do house single people with no children. They have one bedroom flats (all be it in short supply), but they won't house families in those flats because they would be classed as overcrowded. One bedroom flats are allocated to single people or couples without children. So if you can give them the facts of your situation they might be able to help you. I was allocated a one bed council flat, as a single childless woman last year. I had different circumstances to you, but I was not working and desperately needed to move because of some extremely difficult circumstances. It did take nearly a year from when I applied until when I got the flat. If you can show you will be homeless your council may allocate you temporary housing while you wait for a permanent home (it might be a hostel or b&b but it will be safer than where you are now).
You will be able to apply for universal credit to cover the rent and living expenses until you are able to start working again.
I'm pretty sure that by law all councils have a duty to help people at risk of homelessness. They don't have to allocate you social housing but they might be able to give you the deposit for a private let and give you a list of private landlords who accept people in your circumstances. They should also be able to help you apply for benefits and work out which benefits you qualify for. I know that in my area, it's called the crisis prevention team.
Can you go to your local council office and speak to someone in person. Again, I know it's different everywhere, but where I live you can just turn up and join a que to speak to someone at the enquiry desk. If you can do that then do it, and tell them how desperate you are.
I know it's really hard to sort out all of these things while you are under such immense stress, but just take it step by step and get as much help as you can find.
Also do a Google search for charities in your area...you might be able to find all kinds of organisations that can help you. And then contact them all and tell them how much you need there help. You might be surprised by how much help is available if you ask for it.
Also, if you do go to A&E with 'just' bruises after being assaulted....many A&Es have Domestic Violence teams attached and they can come and see you and talk to you/help you. Most A&Es also have mental health Liasion teams who may also see you.
You think you are unworthy of help because you don't have children or you haven't been abused enough yet, but that's not true! You need and deserve help, but you are going to have to ask for it, so I hope you can start believing that you deserve help. Because it will be hard to ask for help if you feel you don't deserve it. It can feel like a battle to get help, because there are so many people in need, so you do need to be quite determined and fight for what you need sometimes.
You sound like a lovely person who is having a terrible time, and you are definitely worthy of being helped. I hope you can find some safety.
I hope I am not sounding like I think it's easy... It know it's not. And I know different services exist in different areas, so there might be less available where you live compared to where I live. I only know about some of things because I have also endured some extreme difficulties in the past, and have had to get help from various services. It was hard and I had to constantly ask for what I needed, find things out myself, chase people up etc. It was exhausting and literally nearly broke me. But if you don't have anyone in your life that can help, then you need to be your own advocate until you find some help.