There's half a chance you're already aware of how the Prime Meridian got to be figured at the location of Greenwich Observatory in London. (If you're a British reader, I'm assuming it's just plain common knowledge.) What you may not be aware of- even though it's the logical conclusion- is that there were other cities in the running to be the Prime Meridian.
Let's build up to that with a recap. In the pre-timezone era of history, everyone just did their own thing regarding time of day. The 24-hour system was in place, of course, but individual towns would judge where the sun was relative to them and create a local time based on that. Which worked well enough before you had transportation options of any appreciable speed or distance, but then the world got smaller and trains were finding themselves reading some downright chaotic schedules. How chaotic? When the railroads made a temporary solution, making 100 different time zones for the United States alone was a vast improvement.
Eventually, in 1884 25 nations showed up in Washington for a conference to get everybody on the same page. Among the tasks was to determine the location of a Prime Meridian. They didn't decide on time zones, despite what you may have heard, but multiple prime meridians were an issue as well. Take a look at this map of southeastern Africa, for example; it's got five of the blasted things. Of course, Greenwich won, on the grounds that 72% of world shipping was already working on charts that centered on Greenwich, making it a path of least resistance.
Ultimately, Greenwich won via vote, and the vote wasn't exactly close. Washington was put forward, Berlin was put forward, Jerusalem was put forward, the Canary Islands were put forward as a neutral site, but ultimately, with 23 nations voting, Greenwich won 22-1. San Domingo (now the Dominican Republic) voted against. France and Brazil abstained. (It has since moved slightly from the marker Greenwich laid down.)
Why did France abstain? Because while they were the ones to raise the Canary Islands as an option, France really wanted the Prime Meridian to be in France. Or at least, they didn't want it to be in England, because France does not like to see England have nice things. After the Washington and Berlin camps dropped out and threw their support behind Greenwich, France saw the writing on the wall for Paris, so they started pressing for the Canary Islands. Once it became clear that it was too late and Greenwich was going to win, they pulled out of the vote. (Jerusalem was pushed by Italy after the conference.) Brazil, part of France's bloc, presumably pulled out in solidarity. San Domingo's vote doesn't show up anywhere I've looked, but also being in France's bloc, one can presume they voted for the Canary Islands.
And then France made their own Prime Meridian, with blackjack, and hookers. They put one in Paris and designated Greenwich time as "Paris mean time minus 9 minutes and 21 seconds". That nonsense continued until 1911, when France finally gave up the ghost, and it took the sinking of the Titanic to get them to adopt it on their maritime documents. But their reluctance was just the most outspoken; nothing settled in Washington was actually binding. Not many international agreements are when you get right down to it. It fell to every individual nation to get the job done on their own time, and they took their sweet time doing it. It took four years for Japan to formally adopt the Greenwich line; everyone else took at least a decade to do it... and when they did, they didn't always agree on whether Greenwich Mean Time was counting from midnight or counting from noon.
Hourly time zones wouldn't come along until 1918, when the United States just did it themselves. Other countries would make their own over the course of the next decade or so; it was never made uniform, so countries have always been free to shift the lines around or consolidate their nation into one timezone or align themselves with neighbors or even go to subhourly timezones (though usually it's the particularly antagonistic nations that go subhourly).
At least France didn't come up with a 25-hour system.