Authoritarian instruction, needed for the days when we fought wars all over the planet. Uniform wearing at school, paved the way for uniform wearing in battle. A natural progression for a nation intent on imperialistic conquering of the planet. The freedom of expression is muted and the typical British stiff upper lip mentality is imbued into the pupils at a very young age. It is the mental conditioning need for a war like nation. Now it is more tradition and the British love a bit of tradition as it is largely a small c conservative nation.
A school uniform is also indicitive of the British class system and the old school tie network is still at large. State schools are deferential to the old Public Schools and try to emulate them by having uniforms that help create their own alma mater. Many things in British life hark back to the days of deference to the Lord of the Manor. Even some simple things. When Capability Brown the great landscape gardener started create gardens at the great country houses, the working class in their deference to what is called "front of house" would highly polish their front door steps as they saw it is a sign of nobility.
