All of these posts and so few mentions of The Knowledge. Its average time to train and pass is about 3 years and is widely renowned as extremely tough. There's a reason so many cabbies are ex-beat coppers - they're some of the few people who know the streets well enough to even begin. You need exceptional spatial awareness and an excellent memory for names and place details*. I've not been to NY so I can't draw any parallels, but from a cursory glance at a map it looks like it has a vastly simpler road network; understandable as London is less of a city and more a product of a thousand years of congealed towns with only the occasional fire or war giving the opportunity for large-scale redevelopment of limited areas.
I've been here long enough to call myself a Londoner, and have been in love with black cabs for years precisely because of the regulation and excellent training. The result of this is that you can give cabbies excessively vague directions (e.g. "a pub about ten minutes walk from station X that has a huge beer garden", "that theatre that was showing Generic West End Musical last year") and they'll still know what you're talking about and will get you there by the quickest route and have to be aware of any roadworks or if such-and-such a road en route is likely to be busy at the time you're driving. I use them because I only ever take cabs when walking, tube bus aren't acceptable (usually due to time constraints) and I've found them unfailingly reliable.
Experience with minicabs has been a whole different kettle of fish; they all rely on satnav exclusively and are useless without a postcode or street/place name - and even then rarely have enough background to distinguish on King's Head pub from another. They'll frequently say "it'll cost you X quid" at the start of the journey and then hold you ransom for "X plus 10 quid" at the end because they ran into traffic or roadworks that cabbies know how to avoid. Given my requirements for timely transport when using cabs, I'll often end up with slightly more money in my pocket but 15mins late using a minicab. YMMV of course.
It's not just a matter of the black cabbies protecting their turf - as well as the knowledge, their job comes with the fairly onerous legal requirements of buying a specially adapted vehicle (hackney carriages are required to have a turning circle of 8m) as well as spot-checks and CRB checks which it sounds like the GLC is exempting Uber drivers from on the basis that the meter isn't tethered to the vehicle. This doesn't really seem fair to me - it's a bit like the government saying that company X has to comply with industry regulations but company Y doesn't because their frob has the dooberry widget on the side rather than the top.
No affiliation with any cabbies, cab firms, cab car companies, cabinets, cab franc, or the Citizens Advice Bureau.
* There are even computer programs for that. One cab journey I made at about 2 in the morning from liverpool street to crystal palace, the driver asked if I'd had a good night and I said no, I've only just got out of work. Why's that? Ah, you work in computers? Wonder if you could have a look at my laptop? It keeps crashing when I hit a speed bump. It was a crummy little netbook but it was running some kind of vastly complicated "knowledge" application that looked like the bastard offspring of a mind map, the A-Z and M C Escher - took about two seconds to see the machine had been through enough abuse that one of the SODIMMs had worked a little loose. Stuck a bit of tape on it and gave it a shoogle, all fine. Cab driver was over the moon as he'd been quoted two hundred quid to have it fixed, I suspect more than the computer was worth, so the journey that would have left me forty to fifty quid lighter ended up being free.