Your main problem here is what is going to be called debt to income ration. This is the amount of debt you have compared to your houshold income.
At present with a debt of around £19,000 and an income of around 34,000 you are servicing a debt to income ratio of nearly 59% and this is most likely going to be in excess of most lenders criteria which will mean a decline. A lender will view a loan of above 50% DTI as unaffordable as it means that the majority of your income per annum has to be used to service the debt and this is not a position that the lenders want to put themselves into as they feel it puts their investment in you at risk.
I do understand that you may not want to approach a debt management company regarding this and I applaud you for this as it is step too often taken and quite often does not solve the problem as many of these companies will line their pockets before they line your creditors pockets. Also be very careful about companies offering IVA's. These are serious debt problem solutions akin to a bankruptcy and while you have hinted that you are starting to have financial problem you have not mentioned that you are at financial crisis which is where I would feel that an IVA has its place. If you take any of these solutions your credit profile will immediately be ruined for several years
Personally I would try and over pay on the debt by what ever amount you can. Debt is not an easy problem and it is a long and slow process to recover from it but it can be done and if you have not missed any payments yet I would urge you to consider this route before any other. By overpaying as much as possible on your debt you effectively reduce your debt balance with the overpayment and therefore with a reduced balance you reduce any potential interest that can be charged on that balance. It won't make a major difference at first but if you can manage even an extra £100 per month this will soon start to make an impact. it will save you an extra £10 maybe but then if you use this additinal £10 towards the debt you chip away just that bit more again and with the money saved you can then pay off more debt.
Looking at your incomes and assuming each person earns about £17,000 this will give you a monthly income between you of around £2,300. If you take out your debt repayment of £900 and rent and other expenses of £1000 then this still leaves you the guts of £400 disposable income. If you can just move £100 towards paying off the highest interest rate debts such as the store cards (often around 34% APR) then you will see the balance come down quickly and the interest reducing. Don't pay off minimum amounts as this will lead to the longest debt, pay what you can and reduce the balance and the interest payable and the debt will clear quickly, then move onto the next highest interest rate debt and start again....it will be a long process but after just a short time youy will start to see positive results. You can do this on your own and with luck your credit record will remain intact....if you use any other method then your credit record will be destroyed by creditors placing defaults against your debts in the debt management programs.
You could also seek help from the debt charity although I am not sure if they can help at this point as you do not yet have missed payments or difficulties, but if the time comes the charities listed below are absolutely free of charge and will work in much the same way as a regular debt management company but without the profit for the company.
National Debtline www.nationaldebtline.co.uk
Consumer Creditr Counselling Service www.nationaldebtline.co.uk
Citizens Advice www.citizensadvice.org.uk
Good Luck