The discretionary payments aren't a huge amount, they are for food and electicity/gas/oil.
There's also benevolent funds you can apply for.
https://britainexplained.com/list-of-benevolent-funds/#:~:text=Benevolent%20funds%20are%20charities%20that,can%20usually%20get%20help%20too.
With interest only mortgage, Free School Meals, Council Tax Reduction, cheaper water and broadband you can reduce the main expenses.
Then you'll need to go through all your direct debits and cut down on the other stuff. You can also check if mobile contracts are out of contract etc.
I use the Money Helper Budget Tool to plan my budget, which is really helpful.
It's shit, but no one is dead, and that's what matters. Mental Health is more important, and you can manage for a few months while things are getting sorted.
How old are the children? Mine are 17 and 18 now. They learned a lot from being skint, and are sensible with their money and their expectations.
We were in a rough patch when I was first a single parent. And again when i gave up my stressful job, and have less money. I've always been open but not scaring them.
The favorite birthday was the picnic in the park with friends not the expensive parties. They look back at the Christmas crafts, books we read etc and the stockings not the big stuff.
You will all be fine, and a well familuly is more important than anything else.