Not quite sure. Unlike US ( at least according to HN readers experience ), most of the booking side features of Uber have been available for years in London. GPS tracking, pre-pay, price compare, ...
I guess the problem is on the driver side. Black Cabs had the same battle a decade ago with the minicabs / private hire. The result have not been bad from a consumer point of view: all minicab service now have mandatory car inspection, driver and insurance inspection checks. I guess Uber style is able to workaround and that pisses off the cabbies ?
Uber is not cheaper than the taxi service I have been using for years. Not quite sure what's the business model of Uber in London and why would people rush to it.
note: The main difference between regular black cabs and other regulated taxi services is that only the Black Cab can pick people up in the street and at Station and Airport pickup points. Minicab need to be booked in advance, which nowadays, means the taxi will come at your GPS coordinates within 10-20 min.
Edit: well according to other comments, it happens. I guess that's why I will never be a startup billionaire, I don't understand people.