If the meter was read and you had an accurate reading when you moved in, I would think 1500 kwh usage during a 6 week period would be high.
I would think that you have the water heater permanently switched on and that could be the reason. And you have really long showers. If you have a high wattage outside light that is permanently on during hours of darkness, that could also be a factor. Change the bulb to a lower wattage or have the light changed to one that only comes on when movement is detected.
At the weekend, what I think you should do, is turn off all the electric items and then check your meter to see if is still registering usage. If it is, you may have a problem, It is not unknown for there to be cross wiring in apartments, especially in converted houses. You would then need to speak to your electricity company about this and see what you need to do. If cross wiring is not the problem, perhaps you have another problem that an electrician needs to check for.