OP, whatever you do, please don't convert unsecured debt into secured debt - that rarely works and generally results in you being in a worse financial position in the long run.
The fact is that your current situation is untenable given the low income and health issues within the family. You are also living in a property that is small and this, and the next few years struggling though a debt payment plan would make me question why ?
If your debt is not going to be paid in full in the next five years, selling the house doesn't just get you out of the current hole, it gives you years worth of breathing space to get things back together.
If you have £100,000 of equity, consider that even with a higher rent each month, it pays that rent for what, eight years and you have released the mortgage payments to go towards clearing the debt much sooner. Or it clears your debt potentially. It also lets you find a property which suits and lets the dust settle with regards to the health of your spouse.
When people talk about the house giving stability, it's from the point of view that hanging on to the house is always worth it. It isn't. You need to consider that the sale of the house may be the sensible approach and be pragmatic about the advantages and disadvantages. I'm not saying that property ownership is overrated but the price for keeping your equity is that you retain a property that you consider tiny, you struggle to make debt payments and you don't have the time to think clearly about how the future is going to work if you husband can't go back to work. At some point the house gets cashed in - either to fund retirement, fund care or fund an inheritance. There's nothing wrong with cashing it in to get out of your current situation and the benefit might be that life becomes more bearable.
I'm not saying that you should sell the house but you should consider it as one of your options. I know it feels like you don't have choices but you do.
How much is your debt and realistically how long is it going to take to repay at £600 per month ? Because that information makes all the difference as to whether selling the house is sensible or not.