Hi Lis496, welcome aboard. I can't really give advise on practical stuff like accommodation, benefits etc as I don't live in the UK. Maybe put up a seperate thread looking for advise on accommodation rights etc, if nobody comes along on here with practical suggestions.
Unfortunately women who had abuse or rejection in childhood are generally destined to repeat those patterns in adulthood. Like you, I learned this the hard way. The thing you really need to hold onto now to help you through this difficult period is that you are changing that pattern for your beautiful dd.
Marriages are indeed 50/50. 'But I was mean sometimes, and had a short fuse, and was generally not always kind. I got angry and upset with perhaps little things.' Nobody walks out of a marriage over someone behaving as you've set out above. People who love each other will work through those issues & in fact far greater ones. You might not be seeing the full picture for now (& maybe you never will), but nobody walks away from a life partner & dd for what you've set out above.
Anyway, the reality for now is that your DP does not want to work on your relationship & so you've got to keep the focus on you & dd 100%. The first step will be sorting out all the practical things like accommodation, access etc..
I would recommend after you've the urgent things sorted that you take time out to grieve & heal from the relationship you've lost. It would also be great if you could get some counselling to deal with your childhood rejection from your father leaving. It might not seem important now but I think it's vital you deal with this when you've had time to heal so that the pattern stops here.
I found it very helpful to post all my madness, sadness, insane rambling etc on here. It also helped to give me a good laugh or hope during times that were very sad. I'm sending you virtual hugs. You are not alone & it does get easier.