Most water companies in the UK will not allow you to start a new flat rate tarriff though (and will definitely be applying pressure to those on a flat rate to get a meter). So if you move house chances are you will get a meter installed straight away if there isn't one already.
I've never stayed in a place in london with a water meter, and I've lived in 5 places over 8 years. In addition we've tried to get one fitted multiple times, as it was becoming mandatory. None of the places I've lived in were able to have one fitted, as in large buildings fitting a meter for each flat is simply not possible, especially in old council flats.