Brozzer .... I am so sorry. You must feel heartbroken.
My ex was a gambler too (though we split up because of his affairs). He was spending up to a £1000 a month at the bookies 15 years ago, and it was only because he was on a very good salary that we didn't get into serious trouble. As it was, we had a crap old car, rotten old carpets, no holidays etc. I tried to reason, tried suggesting a certain, set amount of money each money that he could spend as he wished - but no more, yet nothing worked. Basically, all the nagging in the world won't do unless he wants to give up.
In my case, at least I was a SAHM and I wasn't physically earning the money that was going down the drain. In your case, addiction or not, you are being used and your son is being deprived. To suggest his debts go on a remortgage would never work unless he's prepared to stop all this because you know that he would just run up more ....
..... as Piffle suggested, the only way it might work is if he relinquished all his cards to you, you gave him pocket money and paid all the bills, but I can also see how that could easily lead to him resenting you and it'd be very easy for him to get new cards, set up phone accounts at bookies, borrow off friends and so on and you'd be back to square 1.
Forgive me but you say he's paying £1000 a month on c/cards & loan, and £500 a month at Ladbrookes ...... but he must be taking home about £4000 on £78k pa, so where is the rest of his money going. I'm astounded that you are taking full responsibility for everything except council tax and gas bills (what's that? .... max £250 a month ?). There is a huge amount of "missing" money here.
You've told us what's he's (not) done: Council tax, credit cards and gas ...... but you haven't told us what his reaction to all this has been (apart from suggesting it goes on the mortgage).
Is he contrite ? Does he admit he's been selfish and a liar ? How does he suggest he's going to get out of it ? ...... again, with that sort of take home, I shouldn't have thought that sorting out 10 months of gas and council tax should be too much of a difficulty. Makes me wonder if there's other stuff you don't already know about ...... my ex had telephone accounts with all sorts of bookies .... we'd get calls from them chasing him up for money at all hours.
I know that very few women want to be a single mum but I think there's a very good chance you will dragged down to rock bottom if you stick with this man the way he lives now. There is only so many remortgages you can make ..... and, if you have bad credit, even that idea might not be as easy as it sounds.
You sound as if you're a capable strong woman who is already holding the household together financially all on your own. As for child maintenance, the CSA would assess it at 15% of his net salary per month for 1 child (less maybe some variation if he had child overnight more than 52 nights a year). See csa site . So, you'd be due around about £600 a month.
Whilst it might be explained as an addiction, I still can't help feeling so angry on your behalf 9and your son's). It's such a selfish thing.