santasreindeer, i really feel for you. But i have to say, you are doing amazingly well, you have come from a really hard background and yet you still have managed to settle down with a mortgage and all the stress that goes with it, you should congratulate yourself.
You sound like a fantastic mum, and you are giving your DD everything a little girl needs, and that is her mummies love. How can she be having a shit start to life with a mummy who loves her so much. How old is she?
What sort of work does your DP do?
I think you should talk to your bank, let them know the situation, they may be able to cut you some slack with the mortgage payments. Also, are you getting all the benefits you are entitled to? The benefit system is there to help people like yourselves and you deserve to be given a helping hand. You could definately approach social services for some help with heating, a one off emergency payment, of course i dont think that will cover central heating but they may be able to set you up with something. I didnt have any heating when i had DD1, i was about your age too, what i found an absolute godsend was calor gas heaters. Obviously not for the babies room but for the living room, mine was great and you can pick them up for virtually nothing second hand.
It seems to me you have had to be grown up for a very long time. Another thing that jumps out of your posts and yoru profile is that you are clearly very intelligent. I think you should definately consider going back to college at some point, is there a career path you would like to follow, not now, for later on - i went to college when DD1 started school and ive never looked back.
Try talking to your HV and citizens advice, you have to makeyourself heard as there is help out there but you have to go and find it, if you see what i mean.
Best of luck on the job search. And give your wee bairn a hug from me.