The origins of the school uniform come from Charity schools like Christ's Hospital founded in 1552. In such schools orphans and poor children were educated. They were provided with clothing by the city including a blue coat, leading to such schools being nicknamed "bluecoat schools". The idea of a school uniform expanded during the 19th century often at public/boarding schools.

The justification why I can't explain but at a guess as the education system was often about keeping disciplined and obedient the idea of a uniform like in the army probably had a certain appeal.