Hi there,
Did you take readings when you moved in? And also when you moved out?
It's likely that they've based the bill on estimated readings as they probably weren't supplied them. It doesn't seem THAT excessive, large certainly but it looks like it could be est readings. Your heating was all electric and this does use a lot of supply (i worked in teh complaints dept for a utility firm a while back and that was one of the biggest issues).
If you're concerned that they're charging you for prev occupants electricity, get proof or confirmation of the date you moved in as well as out (council tax bill or a copy of your lease should do).
Lastly, if you're not satisfied with EDF's answer, do NOT leave it there. There's an organisation called Consumer Focus (The new name for Energywatch) as well as OFGEM, so complain to them if you still believe after contacting EDF that they are billing you wrongly.
Hope this helps and if you need any further info just let me know.
Cheers,