British plug design

German plugs have 180° rotational symmetry; it does not matter which way up you insert them into their sockets. British plugs do: you can only put them in one way around, and there's separate names for the live and neutral pins, and different colours for the wires going to them: brown and blue. It wasn't until recently that it occurred to me to wonder: why? These things run alternating current: the electricity runs one way through the wires, then the other way, fifty times a second. There's really no difference between live and neutral. So why do we distinguish between them, and make plugs that have to be put in the right way up (which is not always possible with the design of some plugs or the sockets' location)?