Scarlett -
I had 22k of debt on c ards which I paid off by increasing my mortgage. Like you, I was in a position where I was barely able to keep up the minimum payments. My mortgage was a similar amount to yours, but the property had gone up in value enough that I could pay off all my debt and still leave equity in my flat.
It should be your last resort, but although you'll pay off the debt over a far longer period of time, the amount that your mortgage will increase by will be far, far lower than the amount you're currently paying out per month to maintain your current debts.
It worked for me; the key is to not jeopardise your property and not get back into debt.
Good luck!