Scary situation. You really need some thorough benefits and debt advice - I suggest you go to your local Citizens Advice Bureau and ask them to help you, find it here www.citizensadvice.org.uk/index/getadvice.htm .CAB are better than other advice organisations in these circumstances because you don't just have a debt problem, you also have a benefits sitution and a housing problem and CABs are better placed to deal with this sort of multi-layered problem than other advice agencies.
I am sorry you find it difficult to get out, but this is the best way for you to get all the help you need in one place. If this means your partner is going to have to take a days holiday or even call in sick and miss a shift, then that is what needs to happen.
As it's Saturday, here are some things for you to be thinking about over the weekend. The more you have explored your situation together, the better prepared you will be for talking to CAB. As it's difficult for you to get around, you want to make the most of each visit. I can't tell you what to do because it would need a lot more information than you have given. But some things jump out as being essential right away:
You need to check that you are getting all the benefits that you are entitled to. Use the calculator here www.turn2us.org.uk/benefits_search.aspx - as you will find, it's rather long to go through, it needs to know where you live etc because some things are variable depending on your local council, which is why "advice" on this sort of bulleting board can only be well-meaning pointers, it's not possible to give you figures.
You do need to draw up a very honest budget, looking at what your incomes are and what you are spending. You don't have to post it here if you don't want, but you need it first for your own decision making and second to discuss with CAB when you go and see them. There are lots of budget calculators on the internet, I like this one www.stoozing.com/calculator/soa.php. So put what you think are your real expenditures in there and don't forget to save it, so you can later come back and change it, for example if you starting getting some Housing Benefit to help with the rent.
Sorting out the long term solution to your debts is not the most important thing at the moment - at the moment you don't have enough money money to manage even if you pay NOTHING to your debts. This impossible budget is what has to be tackled first - only when that is resolved are you in a good position to tackel your debts. At the moment you need to be looking for ways to increase your income and reduce your expenditure see debtcamel.co.uk/snapshot/not-enough-to-live-on/ for ideas. The most obvious one is to check you are getting all the benefits you are entitled to, see the calculator linked to above.
But right away you need to stop making ANY payments to your debts. I don't know what the best long term solutions to your debts because you havent said how much each of you owe or what you are studying in the OU or what sort of jobs you hope to get in the long run. But at the moment you can't afford to pay your debts any money, not even a token payment. And from what you have said, there are not going to be any debt options for you that will let you keep a good credit rating, so you should default on all the debts right away to maximise the amount of money that you have whilst you are tackling your "not enough income / too large expenditure" problem. There is more about how to write to your creditors to tell them you can't make any payments here debtcamel.co.uk/debt-options/dmp/ and there are sample letters for you to use here www.nationaldebtline.co.uk/england_wales/debt_advice.php#6 - you want the "ask a creditor to accept token or no payments" letter in section5.
If you owe any money (credit card, loan) to the bank you are using for your current account, you are going to need to open a new bank account with someone you don't owe any money to. If your credit ratings are poor, you will need to ask for a Basic Bank Account. I suggest you go to either Barclays www.barclays.co.uk/Otheraccounts/Cashcardaccounts/CashCardAccount/P1242557963900 or the Co-op www.co-operativebank.co.uk/currentaccounts/cashminder.
When you get a job, you will be entitled to help with child care costs from Working Tax Credit if you are working more than 16 hours a week. You can use the benefit calculator linked to above to find out how much that might be.
re the OU courses. I wonder if you can manage a baby/toddler, working and doing an OU course. Even someone with no depression problems, with plenty of money and no housing problems would find that a really hard period. For you, in a cramped conditions and feeling fragile, it sounds almost impossible. Could you take a break for a couple of years and then come back to it?
re your health. Are you getting help from your doctor? If you aren't, then I think you should go and see your GP. If you are currently on meds, perhaps these could be adjusted? Or your doctor may be abkle to refer you for counselling insetad of pills or in addition to them. These referals tend to take time, so the sooner you start the process the better.
In the end what matters is you health and your family. Everything else comes second. But financial and housing problems will make it harder for you get well. Can you get your partner to read this thread? The more the two of you can work as a team, the easier it is going to be to get through the next few months.
(I don't make any money from any of the links that I give.)