Why didn't Ye Grand Olde Guild of Black Cabbes set-up app-based booking 10 years ago?
As others have mentioned, they did.
It doesn't work as well for black cabs for several reasons:-
1) One of the major conveniences for Uber is the guarantee that the fare you pay will be fair (and the app shows you up front what the expected cost will be) and, most importantly, you don't have to deal with money when the journey ends, you simply get out of the car and say thank you. (If you want to add a tip the app now provides you a way of sending the driver a tip, you can do this weeks after the ride and the driver has no way of knowing who the tips come from, they simply get a lump sum of tips come through every so often.)
With black cabs you never know how much it's going to cost until you ask the cabbie and even then it can vary massively (and it's going to be much higher than a minicab/Uber because of the TfL mandated tariffs). Then you've got the faff of paying (their card machine, which they are obliged to have, is rarely working, see point 2 below) and tip expectation (cabbies saying sternly "You really want the change?", etc).
2) Here's the biggie: Cabbies want to take cash. They don't want card payments, they don't want an auditable trail of income, they don't want taximeters that log everything and upload it somewhere. All because many/most black cab drivers under-declare their income to pay less personal tax.
They are worried that a few card payments will quickly escalate into every journey being a card payment and for those that under declare their income this would mean a loss of income (as they'd bring in the same but pay more tax). Users who book through an app are way more likely to want to pay by card (or even via the app).
Uber provides a full income trail for the drivers, so those drivers can't hide from their tax burden.[***]
3) It's much nicer to sit in the back of a car than it is a black cab.
* Not least the conversation, *anecdata klaxon* but I've only ever had pleasant conversations with Uber drivers and none of the racist/anti-cyclists/etc shit I often hear from some black cab drivers.
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There are a whole slew of other pros and cons of Black Cabs vs Ubers.
The Knowledge is useful, it's nice to just jump into a black cab and say "The Civil Service Club please" and they just know where to go. But...
* Many black cabs have a GPS app (such as Waze, which many Uber drivers use) showing traffic congestion, so they can use that to plot a route around it
* I've seen the Knowledge abused several times. One time the driver specifically picked a route that was full of traffic to maximise his fare, he had assumed that myself and a colleague were out of towners as I let my (foreign) colleague do the talking (they'd never been to London before and wanted to hail a black cab, etc). It was still relatively direct, but had obvious choices to make the time much longer than it needed to be.
* With an Uber you've already given them the destination (although they sometimes ask for the postcode so they can stick that in Waze to get a better route than the Uber app suggests). Setting the exact pick up point is also brilliant, especially for tricky locations that are hard to describe.
Uber's corporate responsibility needs some work. If anything Starbucks/Amazon/etc have proven that the furore over tax avoidance/minimisation doesn't really harm your brand, so there's little point in doing anything other than saying you'll do something about it and maybe pay a seemingly sizeable (but still tiny in relative terms) chunk of corporation tax the next year. Driver's employment rights are another consideration although it is just a great scaling up of how most (much smaller) minicab firms are run. Most worrying is the semi-obvious plan to drive smaller companies out of business (and just convert the drivers over to Uber) with subsidised prices and then, eventually, raise the prices (and bring the company into profitability) once most of the competition has gone; personally I think the driver-less car end goal is a bit of a pipedream that is used to deflect attention away from what is going on right now.
It's very unlikely (I've been burned twice recently on big decisions - Brexit / Trump - so not going for all out "no chance") that Uber will not be granted another license, maybe it'll be another several month extension at first, but I really do doubt that Uber will have to stop operating in London for any length of time because of this. They are already in talks with the Mayor and TfL so I expect something to be sorted out relatively soon. It's certainly ballsy of Sadiq Khan to stand up to them like this (and as the article above mentions several times) Uber haven't had to face up to a licensing authority with this much power and financial backup before, and I'm glad Tfl/Khan have as the other issues (crimes reported against drivers) is a major concern across all taxi/minicab companies (not just Uber).
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*** I wonder who is responsible for the bigger portion of unpaid tax? Black cab drivers (as a whole) because of tax *evasion* by under reporting income from some of them, or the tax *avoidance* of Uber's slice representing the London operation.