I've had a similar issue with BG on the Gas account.
What you need to do, to work out the maximum you should owe is this..
Take a note of your meter reading.
Switch every electrical appliance on, and leave on for half an hour.
Take another reading.
Turn everything off ( or back to "normal" ).
Now, double your reading to get the hourly KWh used, then by 24, then by the number of days you've been in the place - that would be your maximum KWh you could have reasonably used.
Then start to factor things down a little, so work out the consumption of lighting, fridge etc, the remaining being what would be your heating use.
Then "sense-check" it, and talk to the electrcity company. There will be a clause in your rent somewhere that says you're liable for bills, and you could possibly have defaults placed against you ( by the agent ), if you do a runner..