To be honest, she cannot afford the mortgage payments. He was paying for them, and now apparently, he is refusing.
If they have joint ownership it is both their responsibility, so he cannot just bail out. He has to sustain his payments until the house is sold. If mortgage payments are not made, the baliff will be chasing BOTH of them, not just who is living in the house. I would make this very clear to him - if mortgage isnt paid and his credit score is affected, this will impact his future (narcissists like this only listen when it impacts them unfortunately).
I personally wouldnt be staying in the house. I would be applying for a council house ASAP to get myself on the waiting list for the inevitable time when payments aren't made or utilities are switched off.
She needs to apply TODAY for UC if she hasn't already done so, as it can take a while to be paid. If she is unwell and cannot work, she needs a GP note to support this, so she needs an appointment with her doctor ASAP. This will also mean her kids get free school meals which will be another financial burden crossed off.
Next step to do TODAY is apply for CMS for the kids. Depending on his income, this can be a sizeable amount. Again, this can take many weeks to be paid, but she will be entitled to the arrears of the weeks spent waiting.
She needs to contact Womens Aid who can help her in terms of the financial abuse and provide free advice and support in regards to housing, money etc. I believe they or the GP can also refer to a food bank etc so at least her and the kids are getting fed. Too Good To Go bags are brilliant also, and cost a couple of quid - if you are able, you can pick these up daily and leave them in with your friend. Theres usually enough in them to feed a family for at least one meal.
Long term, once she has healed, she should be looking for ways to support herself and her children. This will mean finding a job. She doesnt want to leave this too late. I would say a few months to grieve and heal, then on to job searching. A part time job to start will help to transition her back into everyday life.
She sounds like she is really struggling. I would ensure she has the Samaritans and Lifeline numbers to hand who provide really great counselling services for free on the phone.