I've had many friends whose partners have left and they can not pay the mortgage and bills anymore, child support just does not cover all these things, so your partner has been wonderful to continue to support his ex and child throughout, making sure that even though seperated his daughter has never suffered. You have to commend him for that, he has been a good dad. However, how much longer does it go on, his daughter is now 18, unless going to Uni, she is of an age to now support herself. His ex has had long enough to sort herself out financially, whether moving to a smaller home, getting a job, re-marriage? He should not now be providing for her. He should always provide for his daughter and hopefully will always treat her to things she needs etc. but............
He is in a relationship with you, not a new one by all accounts and his loyalties need to switch, you are in a home with no proper heating, no plaster, struggling, no car, depressed, he is not divorcing and showing any commitment, childhood sweetheart or not, it does not look good to me. He can not keep using his ex as a reason not to commit and put his finances into your relationship, sorry to sound hard, but it all sounds like a cop out.
My advice would be after your op, I would go back to Wales, to be with your friends and family, if not to live with them, property is cheaper there or even a council house, you can stand on your own two feet, (although that is what you have been doing anyway, just in a better environment) a home with no proper heating and no plaster is no place for you and your child. You will have lots of support from people who love you and I bet once happy you will loose your weight. Why struggle financially and be unhappy away from those you love waiting for a man to do the right thing.

You have been patient and understanding enough, for your sake it needs to be make or break time.
Who knows as unbelievable as it may feel now, you may even meet someone else, I wouldn't waste another minute on this man even if I loved him, he does not do what is right by you, you deserve more than that.
The upset of your op would not feel half as bad if your personal life were better, and we all know we heal much better pysically and emotionally when we are happy.
I would seriously look into going back to Wales.

Sending you a massive, huge, big hug (((((((((((((((((( You need it! )))))))))))))))))) Be well soon.