Not read the whole thread so apologies if these have all already been suggested...
You can't change what has happened, @ye10000 unfortunately you just have to pay it. Maybe have a clear out on Facebook marketplace/eBay/vinted to get a bit of extra cash?
Things you can do going forward...
Increase your direct debits so you build up credit throughout the warmer month and the winter bills are less of a shock to the bank account.
Put silver coated bubble wrap behind the radiators or on the back of the garage to reflect heat back into the house.
Put rugs down over any hard floors so your feet don't get as cold!
Thick curtains with linings.
Draught excluders.
Lots of blankets/jumpers/woolly socks, slippers, hot water bottles - heat the person, not the house.
Can you work in a local library/cafe rather from home so that you are out in the daytime so you can turn the heating off for more hours?
Use a teapot/thermos for tea/coffee so you don't have to boil the kettle as often.
I don't personally have one, but lots of people have recommended getting an air fryer instead of using the oven to save electricity.
Shop around in case of any good deals on switching providers.
Hope you are able to work something out with the energy company. It is a stressful time to have to find so much extra, especially as a lone parent.