You are claiming all the benefits you can, I hope? You should be getting child benefit (about 10 pounds pw for the eldest child, a bit less for younger one) and can probably get child tax credit. They're not much but they can help. Can you get a free bus pass for your children't transport? (I know it depends on their age and how far away the school is). You might be able to get free school meals for the children too. Prescriptions should be free if you are on a low income as well.
I know there are other sources of funds too for those who need them. Churches sometimes do food baskets (I know ours does, for example).
Thinking of you.