Consolidating will not take away the debt and will probably just lengthen the amount of time that you are not in a position to buy (as it will probably mean an increase in the length of time you are in debt). It is not a solution to your problems, despite what the ads say.
So, in order to be in a position to look at buying a house, you need two things:
1. Clear your existing debt
2. Save for a deposit/solicitors fees
Prioritise your most expensive debt (probably the credit cards) and pay extra on that to pay it off. Then the next loan, then the one after. As you pay off each loan, move the payments to the next loan, so that you end up paying the same amount out each month in repayments, even though your loans are decreasing. If any of the loans don't allow you to pay them off early, put that amount into a savings account.
It would also help if you said how much each loan was for and what interest rate you are paying on it - in terms of saying "pay this one off first and then that one", but the basic advice always stands - pay the one with the highest interest rate off first, even if it is the biggest and will take a long time. This will save you the most money.
You don't say how much you are currently paying in rent, so it is difficult for people to assess what you could afford in a private rental. It is an option, but I think it would be a difficult step up for you from local authority rents.
I know there are council swap schemes and move schemes, but I don't know the details of them - is there any way you can claim that your current housing is unsuitable for a family with a baby? And see if you can get a move based on that?
Best of luck...