Well, here goes with an explanantion of some of them.
Bilker - Someone who tries (and sometimes succeeds) in avoiding paying the fare for a journey
Butterboy - Nothing to do with Marlon Brando and half a pound of Lurpak. A butterboy is a new cabbie, and since you're new in the job you are "but a boy".
Dirty Dozen - Twelve roads through Soho that get you from Regent Street to Charing Cross Road without having to sit behind several thousand double decker busses on Oxford Street
Flyer - A fare to one of the airports
Gasworks - The houses of Parliament
The Iron Lung - a bloody useful toilet in Horsferry Road SW1
Kipper Season - The time of year when business is a bit slack, supposedly from when cabbies could only afford to eat kippers instead of steak
Legal - The fare on the meter without a tip. You wouldn't do that to a poor hard working honest bloke would ya?
Musher - An owner driver, as opposed to a driver who rents his cab
On the cotton - The shortest distance between to points is a straight line (or at least it would be if you didn't have to drive round buildings and parks to get to your destination. To see whether the route you took is shortest (I'm sure there'll be discussions about "moving lines" later on) you hold a piece of cotton over the map between your start and finish points. If the route you took is close to the straight line, it's described as being "on the cotton".
Putting on foul - nothing to do with dressing up like a chicken, or acting like Christiano Ronaldo in the opposition's penalty area, but joining a taxi rank that is already full.
Roader - a long journey, normally to outside of the London boroughs (note that a cabbie can refuse a fare if it's over 12 miles, or if they think their safety might be compromised. However, if it's 12 miles towards my house at the end of a night shift, it's got to be worth considering)
Wedding Cake - The Queen Victoria Memorial outside of Buckingham Palace
It's just possible that I already use some others and have become a part of my everyday vocabulary, so I don't see them as slang, so let me know if I come up with some strange expression and I'll try to explain it. (Or I might just make something up to see if it gets into common usage - Maybe we could invent this year's "Borange")
I'm also looking forward to picking up new slang expressions, be it cabbie related or otherwise. Just not too much of that Mockney stuff though, please.