Yes - this situation can be 'got out of'.
The most important question here is are his creditors legal lenders? If he's borrowed off Harry Hardman who'll come looking to break his bones then obviously the debt will have to be paid off.
If the creditors are legal lenders - that is banks, store cards, credit cards, legitimate loan companies etc - in certain circumstances (see below), your partner can simply refuse to pay the debts. If, after six years, your partner has made no interim payments towards the debt and has had no contact with his creditors for six years (no interim payments and no correspondence or communication), and if a County Court Judgement has not been obtained by creditors at the end of the six years (you just have to write and ask - costs about £3.50), the debt is considered legally uncollectable and 'timed out'. This does not mean the debt is written off - it means the creditor cannot legally take action to recover the monies owed. Any further action by the creditors outside the six year period is deemed illegal and you could sue them for harassment.
Despite what they threaten in their letters, very few companies actually bother going to court to recover these debts. It's an expensive, time-consuming hassle to them, and every financial organisation has a 'write-off' section. If a CCJ has been lodged against your partner, then that will have to be paid - 50p a week, but most big companies don't bother even applying to go to Court, despite the threats in their letters.
If he is considering signing up with a debt 'consolidation' company - DON'T. If he already has, and he has signed paperwork, get free legal advice online on how to get out of it - fairly simple, just stop giving them monthly payments. These companies charge a fee which they take from the first payments made to them - it doesn't go to repay the loan, it goes in their pockets! They don't advertise that bit!
The 'certain circumstances' can be quite complex, which is why I strongly recommend you look at the websites for Citizens Advice and other free advisory services -National Debt Advice was very good for me, but be careful you're not dealing with one of the debt 'consolidation' agencies - basically if someone asks for a fee, they're not a free advisory service.
There are repercussions: people coming to your door demanding some form of payment - just grit your teeth and say it's nothing to do with you and your partner isn't in; perhaps information gathering from your neighbours - embarrassing but not fatal; he won't be able to 'own' anything substantial such as a car within the six year time frame as it could be seized - but that's good as it means everything of value will have to be put in your name. His credit rating will be shot - he will be turned down for certain credit cards (try Capital One, they lend to anyone!), current bank accounts (try HSBC, again, they'll take anyone!), bank loans and mortgages will not be given. Well, take the view that he hasn't got them now so it'll be no different anyway!
If you marry him, his debts WILL NOT become yours. They were incurred before your marriage. Watch he doesn't start collecting debts whilst you're married though as you could get dragged in then!
If you're looking for light at the end of the tunnel - it is there. Don't despair, there are loads of excellent organisations designed to help you available online and on the phone. If you simply don't know where to start, contact the Samaritans - they'll know who to put you in touch with. As you've got housing issues as well, contact Shelter - they're not just for street-sleepers - they were brilliant when I was in trouble.
Priority - put yourself on the Council housing waiting list as a single parent - you can decide if you want your partner to move in with you if and when you get offered a decent property. If the lease of the council property is in your name only, if he does go mad with the money again, you can just kick him out with no material hardship to you or your child.
I wish I could give you a big hug - you sound worried to death. Don't be - it's resolvable - boring, but resolvable. And if your boyfriend can time his debts out, you'll even have money for clothes for yourself. Without holes!
Very best of luck.