I rely on mini cabs in London and I can tell you Uber are not cheaper, they're often more expensive and take longer to arrive.
I think one anecdote is not indicative of anything, especially considering the market share they now have in London.
For a counter balance, whenever I am in London I use Uber the same as I do in my local city, all my colleagues from London wax lyrical about how much cheaper/quicker and in some instances cleaner than the mini cabs or black cabs. Our company and many others I know use Uber as it can offer a centralised audit trail for expenses purposes, but then again we are multi national tech firms which I am sure someone like RedToothbrush hate.
I think they will get there stuff together and get re-licensed, if they do and do not get re-licensed it shows how a lot of people are seeing it that it is purely a political move, which could backfire.
Also I will add a caveat that I'm not too keen on Uber as company but I admire that they are trying to be first to market as there business model is based on driver less cars, if they do not take off then the business model collapses. As for a pp trying to scaremonger about them saving journey data, there a millions wilfully giving it up anyway with the location data on phones, checking in to places via facebook and if TFL get the backside in gear they will be offering an App that does the exact same thing which will be farmed off to some third party big data vendor, its the way of the world now.