OP I feel your pain, I live in London too and everyone round here is frantically extending upwards, outwards, sideways and downwards. One of the people in my street did all of that in one (very long) building project. Of course they lived off site....
I've looked up the Sunday Times article that Lonecat mentions, have pasted the top tips below (they are for the people undertaking the extension but still helpful in terms of questions you might ask them).
Top tips
DO let your neighbours know your plans before starting work, and warn them about any possible disturbance you might cause
DO find out if any neighbours have already completed basement excavations, and whether there were any stumbling blocks
DO get your structural engineer to conduct a full survey of what is underneath the house before you start any work
DO check any prospective contractor?s credentials and ask for references from past clients
DO ensure they are fully available to oversee the job and won?t just be popping in now and again to oversee less experienced builders
DO line up somewhere else to stay as a respite from the chaos in your own home
DO consider how you can maximise your basement space ? for example, creating an extra bedroom ? to add value to your home
DON?T assume that anything will be straightforward. Prepare to be flexible with your budget, problems that might arise and how long the work will take
DON?T pay in instalments, if you can possibly avoid it. Try to agree on a figure up front, payable on completion of the work
DON?T go ahead without a legal contract with your builders, highlighting any problems you know of.