I disagree about the bank offering you a split.
If you are due to repay 2200p/m and only earn 2370p/m, it's a no brainer.
You are insolvent and will have 170p/m to service all utilities, feed your family, dress them, live, travel to work, pay for medical etc.
You will be offered a split or it's a lose situation for the bank. A voluntary sale, minus legal costs, will see them lose a hell of a lot.
Your house value could be lowered to the 200k mark leaving you with 100k of negative equity.
Propose to the bank a split with that amount parked.
You would prob be paying around the 1600p/m mark with the 100k warehoused.
That would leave you with 770p/m to live on. Still well below the Reasonable Living Expenses in a Personal Insolvency agreement.
I'd imagine they will push out the term of the loan too, if possible.
What ages approx are you both? IS this possible? what term is left on the current loan at present?