British Gas - advice

SwanJon

It might just be that you have more external wall than before, and aren't benefitting from living above someone else.
As above, the insulation is going to be different too

How frequently are you taking readings? It might give you a better idea of waht is using the gas/electricity (and avoid bill shock!)
Have you checked that the gas meter and gas bill are counting the same units (bbc link in Wywth's post).

Have you had a chance to look for the best tariff/supplier for you? It's always polite to inform your LL, but you pay the bills so you get to choose.

Fire_Fox

Flats generally benefit from neighbours even if the windows are drafty, end of terrace has a lot of outside wall and roof compared to the volume.

Are you sure you don't have an electric immersion as back up for your gas hot water and it's on all the time? Either timer is not set properly or thermostat broken say. If not check the meter is working correctly, turn EVERYTHING off except one item with a known wattage, and take readings before and after.

It is possible you are using 15KWH a day tho, especially if you have a power shower, depending how long you call 'short'. There is a good chance the washing machine and dishwasher are cold fill - what temperature are they running at and whether using long or short washes is relevant. 'Not much' tumble drying is still some. What KWH are you averaging on days you don't use the washing machine, tumble dryer or dishwasher? Your lighting and TV watching is largely irrelevant, it's the above that are the energy guzzlers.