Why does the London Underground use two live rails instead of just one?

From http://www.trainweb.org/tubeprune/tractioncurr.htm :

Current Rails

All London Underground Lines (including the W & C) operate at 630 volts DC using third (positive) and fourth (negative) current rails. The current rails are positioned so that the contact surface is higher than the running rails. This allows the collector shoes on the trains to pass over the running rails without touching them. The positive rail is 3 inches higher than the running rails, while the negative rail is 1.5 inches higher. The positive insulators are thus twice the height of the negative ones and therefore have about twice the earth leakage resistance, so the voltages are set with a proportional disparity between the positive and negative voltage levels. The positive rail is at a potential of 420 volts above earth and the negative rail at 210 volts below earth.

Why 4 Rails?

The London Underground uses the four rail system for two main reasons. Firstly, it was originally required by the government to limit the voltage drop along the line to 7 volts. This was intended to reduce problems caused by stray currents causing electrolysis affecting utility pipes and cables. Whilst this did not affect the street tramways, whose vehicles were not heavy current users, the currents drawn by trains could cause difficulties. The solution was either to provide heavy return cables and boosters or to use a fourth rail. The fourth rail was chosen, partly as a cheaper option and partly for signalling reasons. As direct current track circuits were to be used to control signals, an insulated return system for the traction current was an effective way of separating the two systems.
Nowadays, this is not so much of a problem as all track circuits are AC.

The National Rail areas that use a third rail have the conductor at a nominal +750V and use the running rails as a 0V return; however, it is still not considered 'safe' for untrained people to be on or about the track...

This addresses one of you sub-questions from a different point of view to AakashM's answer, which I recommend reading first.

Why not use 630 V and 0 V? Wouldn't it make one of the rails safe for people?

It would, but the area where the rails are would still be a very dangerous area, both from electricity and from the trains it powers. A tiny reduction in a huge hazard isn't much use to anyone, and if it increased the risk of faults even slightly, the overall risk may go up as fault-finding isn't risk-free.

Using +630V instead of +420V is indeed a possible option, and it would make the railroad equipment somewhat simpler and safer. This is what is often done with household electricity in most countries, where only one wire is "live".

It would require better insulators to cope with a higher voltage though. Perhaps such insulators were not available or too expensive when the first railway sections were built, so the voltage was split. And once these first sections have set a de-facto standard, other sections were respecting it for compatibility, even if high voltage insulators became available.

Splitting equally (+/- 315V) would have been better from electrical standpoint, but it seems that the higher height of the 420V insulators is useful in itself, as it prevents the 420V collector shoes from accidentally touching the -210V rail, which is lower.