Race The Tube - Sprint

Someone managed to run between them actually, leaving the train at Mansion House and catching up to it again at Cannon Street! [VIDEO]

Sorry, but I don't think some of your assumptions make much sense. Tube train tunnels are large. If we were developing some alternative method of transport, why would we reserve the entire cross section of current tunnels for single occupancy vehicles? As demonstrated by the Tube itself, much higher densities could be achieved, even with private vehicles, either by having multiple people per vehicle or by using smaller vehicles that didn't require as much space and could run alongside others. Of course density isn't the only thing that matters. Consider that the average speed of an Underground train is about 20mph. A fit person can run faster than a Tube train moves over short distances.[1] Clearly if you had a system where loading and unloading happened without blocking the main tunnels, significantly higher speeds could be achieved over the kinds of distances a typical passenger might be travelling. [1] No, really! [VIDEO]

There's a handful of stations on the tube where above ground they're but a few minutes walk even though underground the train takes much longer (and I believe I much more circuitous path). IIRC you can actually jump out at the platform and run above ground to the next station before the train arrives. Edit: Here's a guy racing the Circle Line from Mansion House to Cannon Street [VIDEO]