@medianewbie
TBH it doesn't matter how "modern" it is - what is the power rating?
Your gas usage doesn't seem anything out of the ordinary but while your gas usage is similar to mine your electric is 3x what I've used in December - it's definitely electrical appliances and usage that need to be looked at.
As @user143677433 said - I also found that my 20+ year old fridge/freezer was using about 25-30% of all my electricity and you also have a chest freezer.
We use the dishwasher 2x a week (only 2 adults in the house) and the washing machine 1x a week - no tumble drier - we have an overhead airer in the utility room where the gas boiler is. Can you check your dishwasher is set to 30C - we just use better/more expensive dishwasher tablets and washing at 30C is fine - it wasn't with the cheaper tablets.
Remember that Dec, Jan and Feb will be far more expensive than the other months so my December bill
Gas 2335 kW.Hrs x 10.34p/kW.hr = £241.44
Gas standing charge 28.48p/day x 31 days = £8.83
Total = £250.27
Elec 216 kW.Hrs x 35.98p/kW.hr = £77.72
Elec standing charge 48.59p/kW.Hr x 31 days = £15.06
Total = £92.78
Your unit prices (kW.Hr prices) are slightly higher. Your daily rate is higher but really the standing charges don't amount to much compared to your usage costs.
How much do you use your oven? We barely use ours now - possibly once a week, maybe less. Look at December's electricity usage and see what a difference the cooking on Christmas day made.
So my bill for Dec may be £250.27+£92.78 = £343.05 but my current monthly payment of £177 has still left me in credit by £635. Are you currently in credit or debit with your supplier - can't you look at that on-line?
I'm sorry you are so upset and worried about this - you really need someone to come in and look at what you are using and how often to see of there are any changes you can make to the way you live. It's possible you are overlooking something or some appliance is actually costing you a lot more than you think; the devil's in the detail. The other thing is that you need to look at insulation in your loft - I have actually velcro'd some foil bubble wrap on many of my windows (normally you place it behind radiators) - OK it looks strange and stops light getting in but it's not every window and at this time of year there's not much light anyway - the house is definitely slightly warmer and I only set the heating to 17C during the day turn it down to 15C at night. Do you have an upstairs? Heat naturally rises so it will escape up the stair, under doors, through any gaps - heat that you have paid for - at the very least throw a big old towel or blanket down at the bottom of a door leading upstairs. The truth is - few people can afford to do nothing about the cost of energy ATM. Jan will most likely be colder than Dec and Feb possibly just as cold so you need to take a hard look at what you can do - even if it means spending a bit of money to save some. Do you really need that chest freezer? Hard decisions need to be made.
I hope your situation is either not as bad as you fear or that there are some easy changes you can make. You are not alone - there are plenty of people struggling - I know my neighbour is stressed about her energy usage ATM - it's a regular topic of conversation.