My understanding of this is that, when Japan was setting up their education system during the Meiji Restoration they wanted to emulate British schools, which at the time were going through a big movement to adopt uniforms in order to instill kids with morals or something. Since this was that weird time at the turn of the century when everyone was dressing up their kids like sailors that was just one of the uniforms they used, though they later fell out of fashion. But when I went to confirm this I couldn't really find anything solid. So I was wondering:
EDIT: It's been a couple hours and still no answer. I know it's an obscure question, but surely there must be somebody on the internet who takes an interest in Japanese schoolgirls
I know your question was particularly related to "school girls," but you may want to be a bit more specific. Uniforms differ significantly between elementary, middle, and high school girls. And because each school tries to make their uniforms uniquely identifiable, there's significant deviation even at the same level of school.
I'm going to assume you mean the stereotypical blue sailor collar, typically middle school girl's uniform. But it's important to keep in mind this uniform is not ubiquitous. Many don't use the sailor collar at all anymore, and have switched to simple blazers and skirts instead -- especially at the high school level.
"Sailor" style outfits for children were popular on and off from the 1890s all the way up through the 1930s in both the US and the UK. In the UK it was usually referred to as a "middy" top (from "midshipman") and was popular with girls under 14. However, schools in the UK were not that fast to adopt new fashion trends, and the middy-style top was not broadly used as a school uniform. So we can't say the Japanese version was taken from the British education system.
Rather, the sailor style school uniform was invented in Japan by the head of an all-girls Christian religious school in Fukuoka named Elizabeth Lee, originally founded by American Methodist missionary Jennie Margaret Gheer. She was tasked with designing a distinctly "western" style uniform for her school, and she pulled from her idealized memory of "middy's" from her time as an exchange student in the UK.
And from there, it spread to other schools just because a lot of people thought it was stylish.