Hi
The bill could be correct if the immersion heater has been switched on constantly. Once the temperature reaches a certain level, it will switch off, but the heater will keep on switching on/off keeping the water hot. From previous experience a typical immersion heater will take 60 to 90 minutes to provide a full tank of hot water. The water will keep at a reasonable temperature for a day, unless you have a bath. This is a very expensive way of getting hot water. My great aunt left her immersion on constantly and the quartely bills were very high. Also we found that her flat also paid for the electricity of a light in a communal area of the block of flats. It is worth turning off all your electrical items and then checking the meter to see if it is still showing usage. If the wiring to the flat has not been done correctly, you could be paying for other peoples electricity. Your neighbours might not realise this but could be enjoying cheaper bills. We had southern electricity check our aunts meter but this was found to be working ok. The engineer said it is very difficult to prove if a meter is faulty and would be fairly costly to have electrical system independently checked. The reason we had the meter checked was that had found that 1 outside light was costing about £20 a month. My aunt was not resident at the time, so we turned off the electric. We were not going to pay for the neighbours to have a lit communal area.
As you say the system look old, I wonder if it is in safe working order. You can find more information searching online about tenants rights. The following has been cut and pasted from one site.
The landlord is responsible to maintain installations for the supply of:
This would include cisterns, radiators, boilers, heating ducts, water tanks, baths, sinks and all the pipes for gas and water as well as electrical sockets and wiring throughout the property.
I don't know what your current position is with regard to a shorthold tenancy agreement and whether your landlord is using a letting agent. I would get in touch with Citizens Advice who will confirm what your rights are. There are many laws which apply to tenanted accomodation and you may be able to request action from your landlord. An electrical system check and upgrade of water heating system would be a minimum. Your local council authority may also have powers even if it is a private landlord and not a council funded let.
Warning. Do not withold rent or take any action without getting advice first. Make sure you are on safe legal ground first, as some landlords I understand can be very difficult. They don't like having to spend money fixing properties.
Good luck
Huckster