Hello again and thanks for the extra information.
re buying a new house
As your total annual income is £42,000, the maximum mortgage you are likely to be able to get is £168,000 (but it could be less as it's getting more dfficult to get a mortgage these days). As long as you are jointly and severally liable for the £160,000 mortgage on the house you own with your ex, you will not be able to get another mortgage, because that uses up all your mortgage capacity.
re: your ex buying you out
As there is no equity in property - in fact the property is in negative equity as the mortgage is higher than the house is worth - there is nothing for her to pay to you for your share.
The only way for you to be released from your liabilities under the terms of the mortgage deed are either for your ex to take over the mortgage into her sole name, or for the house to be sold.
To take over the mortgage, your ex will need the agreement of the buidkling society (or another building society) – but she will not get it as her income is too low. Her mortgage capacity is at most £80,000 – far too low for a mortgage of £160,000.
If the house is sold, there is no equity, so neither of you will recieve anythign from the net sale proceeds – instead, there will remain an outstanding debt of £160,000 - £137,000 = £23,000, which you will both be jointly and severally liable for.
You MIGHT then be able to get a mortgage of £168,000 - £23,000 = £45,000. But your ex would have to rent with the kids.
Another option would be to agree to continue paying the mortgage until the your youngest child reaches 18, at which point you agree with your ex that the house be sold, and the net sale proceeds divided between you. This would mean that you would have to rent until then – but at least your children would not have to leave their home.
You do need to check out what arrangements if any were put in place to pay the capital sum at the end of the mortgage term, such as an endowment policy – because that might give you both a bit more leeway if whatever it is has a surrender value now.
If you and your ex can reach agreement, a solicitor can put that in writing for you and advise on whether or not a court order by consent can be obtained to make your agreement legally binding. Anyway, I think you would benefit from some face-to-face legal advice. Here's where to find a specialist family law solicitor:-
I know you were hoping for a more positive answer, but it would be wrong of me not to be honest with you.
I hope this helps anyway and I wish you the best of luck.
Thanks and best wishes...
PS With regards ***** ***** you pay once you accept my answer - which I hope you will do!