The interesting thing is, pedestrians in the current day Tokyo/Kanto region and most of the country pass each other on the left side (e.g. on escalators), but if you go to the Kansai (Kyoto-Osaka) region, where samurai were not as prevalent as they were in Edo, they still pass each other on the right. So it's likely that whoever made the transportation decisions in the early Meiji period were former samurai.
Another theory is that the new government leaders simply went by what the British did because the British government actively supported their cause when they were trying to bring down the Tokugawa shogunate, but I'm rather skeptical about that since the once the new government took over, they took ideas from several European sources. The parliamentary system was based on the Prussian model for example.