It’s does sound like it’s the old wiring, as you are not using that much kWh elsewhere.
The only other thing I can think of, did the person who read the meter read it right. Can you read your own meter?
My bill before last one was read wrong by 1000 kWh, I read it myself and had reading on the bill changed to the right reading. My last bill was right amount so I was right.
I find my kWh chart, post part of it as it's now has 14 years of figures on it.
