As it's a 3 storey house I assume it's quite big - say 4 or 5 bedrooms. The figure doesn't look all that unreasonable to me. My house is 2 storey, 4 bed and the figure is around 4750 Kwh.
You could look into possibility of insulating (particularly the loft) and if the boiler is pretty old it's probably inefficient compared with a new one. However, as you are renting you are not going to want to pay the costs for any such improvements, & it may be that the landlord wouldn't agree to pay for it either.