The costs of doing a house extension depends on a lot of elements. One of the main things is: how big are you planning your extension to be? Doing a smaller house extension by adding just one room will cost less compared to a house extension in which you want to add two or more rooms to your home.
House extension cost is also based on the type of your house extension. It is hard to say which type of a house extension single story extension or two story side extension will cost less because the prices of such house extensions are also related to the scale of the project.
Nevertheless doing a house extension in London is a pretty good investment as any additional room can increase the value of your property significantly.