I’d imagine you’ve thought of these but, trying anyway :
With your kids, some GPs will prescribe multivitamins.
Then for menus :
Proteins : eggs are the cheapest, so mostly that ; meat buy those absolutely huge roasts etc when they’re on sale (the day they’re before out of date) ; as pp mentioned end of days are good for that, they’re going to be thrown away so they get even more reduced : prepare and freeze ; and especially, small portions are just fine enough, no need for what you’d consider previously reasonable size
Veg : huge bags of frozen of the same ones, either you have a huge freezer or too bad it’s the same one for the week
Fruit I don’t really have a solution tbh, count on the multivitamins and hope for sales on seasonal ones
Then absolutely load on cheap filling carbs, there’s no need to feel guilty about it, they’re getting a balanced diet
Bread : making your own is much cheaper, and easy.
All of this is much easier for a large size freezer naturally.
Electricity : cheap desk lamps for the kids for homework (you can minimise the miserable aspect with fairy lights, you can get huge ones for like £1 on Amazon
Buy in huge huge bulks candles, for either if you’re really really skint, or even worse the electricity gets cut off. They do reasonably last, just buy really large quantities (Amazon)
Baths : depending on the balance, you can heat a large pot of water on the stove for baths
Gaz : woolly hats and scarfs and socks at home do make a difference (primark or wherever)
And don’t worry your kids won’t be traumatised : my mum used to f*ck off with her next bf for days leaving me to take care at 16 of my 9yo brother with no way enough money. It’s just about presenting it to them in both a realistic way (it’s difficult times for everyone ; maybe an age appropriate video like UNICEF of kids who walk ages to school (I walked him to and back to school 1h round trip for me, and presented it to him as his exercise for a healthy heart), don’t have medical care etc). Do try to make it a little fun ex fairy lights, candles are cool, that kind of thing
Dont know if this helped in the slightest sorry