I agree with applying for the warm homes discount if you have not already, it's actually worth changing supplier to get it and the price comparison sites allow you to search for it.
It is £140 towards your electricity bill. There is a 'core group' who automatically get it but then there are other groups that the power companies decide who is entitled. There is a finite amount of money so it is first come first served.
Yes to Olio and 'to good to go', Olio is great people put small amounts on there eg a loaf of bread. You could ask for a bottle of milk. People also put up non food items.
'To good to go' is a selection of groceries, you select a bag and pay for it and then collect it in the time slot allocated, it's mainly groceries going out of date and depends on the shop so a bag from greggs will be sandwiches, bread and pastry.
Also some pubs near me do a carvery to take away.
Some places have 'pay what you can' markets.
Check out any funding you may be entitled to, local charities may be able to help with one off amounts eg to repair a boiler.
My parents used to be members of 'St Vincent dePaul', now it is an RC charity but one thing they funded each year was a holiday for a family in need. It was usually a week in BUtlins with travel and packet money, it might be worth considering next summer.
Do you have a Sikh temple near by? You can get a free meal as it is the duty of Sikhs to feed anyone whether in need or not, you can also volunteer to help if it feels a bit cheeky.
Do you have a tent? It might sound crazy but a tent inside the house can make a cosy place to sleep and is fun for children.
When it is really cold you might consider all sleeping in the same room so you only have that room to heat. I know it's not ideal long term but you could do a 'family sleep over'.
As door bills and arears, well they can't cut of power and water if yo have a child or a disabled person in the house. And the various companies all have departments to deal with vulnerable families.
I'll be back if I can think of anything else that might help.