I only tried Uber once, in Paris ... it was a bit of a disaster.
In London I only use Black Cabs.
When my little brother was ill, we were blocked in as the London Taxis were protesting the minicab rank in Victoria. The police couldn't help, nor could an ambulance get through - I phoned the various Black Cab booking services, Radio Cabs and Dial a Cab, etc, and they all very kindly moved so that I could drive him to the hospital. I still cry every time I think of it, and their goodness will always touch me.
Mini cab drivers are unsafe and unregulated.
Last year I kept catching an Addison Lee driver parking and wanking - windows open, opposite a school. The police tried to stop him, but the guys who did? London Black Cab drivers.
London taxi protest: Gridlock in central London as cabbies bring traffic to a standstill - London - News - London Evening Standard
The best advice I can give anyone visiting London is to get an Oyster Card as public transport is easy outside of rush hour, and to only take Black Cabs - minicabs can sometimes sound cheaper, but they often turn out not to be, and your safety is worth more than a 'bargain'!
Black Cab drivers know where they're going, they're safe, they're professional - and they're Londoners so they help you with a problem.