In addition to just memorizing facts, they are building a mental structure for all the connections within the city. I wonder if learning the structure of any large system would have the same effect? For example, a large software system, the economic system, or the political system -- where you understand the relationships of all the political players.
Perhaps the political system, or a complex ecosystem with a lot of relationships, but I think software and economic systems are generally much less complex than London. The thing about a city like London is it's pretty much 'incompressible' data. If you want to learn New York, large chunks of it compress by saying things like "the roads are mostly a grid", "these streets are numbered sequentially", etc. London doesn't show that kind of patterned, designed structure that allows other complex systems like software systems to be learned. Imagine trying to learn Unix when anything that would be referenced by a number is referenced by its own name.
Also cabbies need to know traffic patterns for the city to get around it quickly, which means in principle you're learning what the traffic is likely to be like on every road on every day of the week. That's a lot more compressible though.
