Just a data point: this is not my experience, nor that of my many London Uber-using friends. We exclusively find it prompt, reliable, and drivers are courteous to the point that some offer to play the passenger's choice of music, give them lollies, etc.
An Uber-XL will happily carry a bicycle or large amounts of luggage. And I've not once experienced an Uber driver refusing to take me anywhere. "South of the river? Not at this time of night guv". Pffff.
Black cabs are now campaigning and many rally behind the slogan "the safest ride with the greatest guide" (from memory). This betrays how fundamentally they have failed to understand the trouble they're in.
Safety: Uber purport to address this with registrations and reviews. (This may be fallible, but no more than black cab registration).
"The greatest guide"?? Puh-lease. Nobody but nobody wants their cabby to be a guide, nor to offer their opinions on anything. Perhaps a tiny minority of tourists may feign interest for a few minutes. Perhaps.
Unfortunately for black cab drivers, it seems that the current generation have sat cosily on the monopoly they inherited, and they've been caught napping.
None of this is intended as an anti-black cab rant, I simply think they're failing to deal with the primary issue: the times they are a-changing.
Edit: typo.