Sorry you are struggling OP, but something isn't right here, there has to be a lot more to this than the simple cost of your DD going up. If your illness is stopping you from sleeping during mild weather and enough bedding to camp outside in winter, is there anything your GP can do?
Plus your house shouldn't be getting that cold at the moment, where are you in the country, it's been quite mild recently, our heating is on a Hive thermostat and has barely been on for weeks.
I know bills have gone up, but if you're in a position where every last penny goes on bills when you have good jobs, do you have debts? If so and debt repayments are taking up so much that you can't afford the basics and you certainly can't afford for your DH to go to the football if that costs money that could be a trigger for getting advice on resolving the situation. Do you own or rent and what's your heating and insulation like?
But on the matter of the cost of heating, paying by direct debit means that you shouldn't expect to pay less at this time of year because you pay an average amount all the year round, so your actual bill might be something like £80 for April, but £400 in December, but you also need to check if the £265 is the right amount. It could well be depending on your circumstances, many people will now need to be paying quite a bit more than that, in larger houses, lots of electric showers, tumble dryer use, poor insulation etc.
But you need to check by taking your annual consumption which should be on your bills, or look back over previous bills to find out, and multiply by your tariff (it looks like you're on the SVR which is good as there have been some fixes on offer recently that have been far more expensive than that). Also take into account any debt on your account.
Use all that info to check whether the £265 is reasonable to pay for your average usage, pay off any debt, and possibly get a little ahead going into winter, because what you don't want to do is underpay and end up building a bigger debt next winter and face even bigger bills. But if the £265 is too much, see if you can reduce it in your online account, or give BG a call, because some companies have been hiking DDs to more than needed for the customer usage.
But it sounds like you might want to look at your wider financial picture because you shouldn't be struggling as much as your OP implies.
Have a look at the Moneysaving Expert money makeover to go through all your bills and spending, to see if you can reduce the cost of any essentials, identify any ways that money is leaking away unexpectedly and get signposting to further help if you are in debt.
www.moneysavingexpert.com/family/money-help/
Good luck 