I have just given my first meter reading but it has been back dated to October, as I moved in in the middle of December will I be charged for the electricity the previous tenant used
well you should have given an initial reading when you joined. That is when you start paying. Get in touch properly and provide proof of when your tenancy started and stick to your guns
On the day that you became responsible for your new home did you provide a meter reading to the supplier of the property, was it Bulb?