They cite passenger safety concerns, but there's been not-too-subtle protests by Black Cab drivers who simply refuse to change their archaic business model and a very stark lack of actual Uber users concerned about safety. Not only is it far less convenient than Uber, calling a Black Cab means you need to venture onto the street and if you're not in central London you're basically stuffed. There's also the matter of cabbies being many times more expensive than Uber - a £20 Uber would be £50, at least.
The Black Cab drivers are being petulant children about it. I'm sorry their livelihoods are under threat but they either need to evolve or die. They literally blocked off a major London road right outside my offices in protest against Uber a few months ago; right off Blackfriars Bridge they parked horizontally in the middle of the road, causing absolute mayhem. Usually I'm fine with people striking, but there was no legitimate grievance here - a better competitor came along and instead of embracing change (and progress) they simply threw their toys out of the pram and demanded the politicians (who are in their union's pocket) simply get rid of their competition.
The politicians didn't take much persuading, and just like that we rolled back to Black Cabs (which half of Uber users were priced out of in the first place). Unions are generally a force for good, but this was just a shameless attempt by the Black Cab union to have the competition erased, where previously they operated in what could easily have been described as a monopoly - previously they only faced competition from minicabs and Addison Lee, which largely had an entirely different customer base.