Gas & Electric
British Gas has some of the most competitive gas and electricity rates in London. You should plan on anywhere from £30 to £100 per month per flat for gas and electricity expenses.
http://www.britishgas.co.uk/
Water
Thames Water provides water in London. There are two types of payment plans. One is a fixed fee paid twice per year (appx. GBP 450 per year per flat). The other requires Thames Water to install a water meter in your flat. This fee will obviously fluctuate with the amount of water you use. If you go to their website, they have a tool that you can use to estimate your water usage and thus your monthly water bill.
http://www.thameswater.co.uk/