First of all - DUMP British Gas...they are typically the most expensive of the 'Big 6'. I recently found out that Sainsburys Energy is actually British Gas in disguise, but tons cheaper. Use a couple of the comparison websites. We are with E.ON, and have a very competitive fixed rate with no exit fee if E.ON offers a better rate, and a modest fee to switch to another supplier.
Sign up for an on-line AC if you don't have one, and submit meter readings monthly. And...think about the thermostat setting. IMHO, 15 is fine at night (we are OAPs and still turn it off at night). During the day, try 18 or even 17, and wear a fleece top. If you are moving around, taking care of kids, housework, whatever, you should be warm enough at that setting.
Check the insulation in the loft; even if you are renting, it may well be worth the £ to add some insulation if the landlord won't do it. If you own the flat, you will reap the benefits of loft insulation and there are schemes around from time to time that offset the cost (which is minimal compared to the energy savings).
If you have gas heat, have the boiler serviced, or again, if renting, have the LL do it if it's been more than a year. A tweak here and there can make a world of difference. If your heating is electric, it's likely to be more expensive than gas, so look at closing doors to unused rooms, making sure the heaters aren't dusty etc.