The simple answer, then, is that black cab drivers are tested on successfully fitting in with the flow on bus lanes so that they don't slow down buses, and minicab drivers are not.
> 3) I used to drive to and from work every day. Part of the journey took me along the A4/M4 towards Heathrow. There was a traffic jam every day, going home from work (towards Central London). This busy road had a bus lane. I don't recall ever seeing a bus going past me in that lane, but plenty of black cabs did. I don't see why a black cab should get to skip past the rest of us waiting 20 mins in traffic.
As for black cabs, perhaps it would be a complete hassle to implement a "no black cabs" rule for that one road just to avoid upsetting people who chose to drive into London.
There's all sorts of potential reasons for that bus lane existing - and there's a very good chance that if someone were to file a FOI request with TfL, they have a report on the potential results of removing that bus lane.
It's a well-known controversial bus lane, which became a political issue. Anyone complaining about it loses my respect on HN, as they didn't look at the traffic engineering problem, just the Daily Mail hate.
The motorway is 3 lanes until the final stretch into London, which has two lanes. The width reduction isn't at a junction, so the extra lane didn't help traffic flow -- it just caused congestion and collisions by making drivers merge. The lane was ended at the preceding junction's slip road, and a bus lane continued for the spare length. This improved journey time for buses (a minority of vehicles, but a decent proportion of people), and also improved journey times for cars!
But, the sight of the bus lane annoyed the Tories, so they got rid of it.
https://en.wikipedia.org/wiki/M4_bus_lane
https://waronthemotorist.wordpress.com/2010/11/22/the-m4-bus... is where I first heard about it (I lived in London at the time, but didn't have a car.)
That's an argument to get rid of bus lanes, not to allow some protected class of cars to be permitted to use them.
Anyway, bus lanes aren't about reducing congestion overall, but reducing the congestion faced by users of buses.