The traditional prepositional phrase is on foot.
Céline’s bicycle broke down, and she had to go to work on foot.
The increasingly common by foot is also accepted but is used much less
commonly. It is useful for parallelism when several methods of transportation
are listed with the preposition by.
Tourists visiting China travel by train, by airplane, by car and by foot.
https://reurl.cc/XqvXxj
“On foot” and “by foot” have identical definitions: “walking rather than
traveling by car or using other transport”—Google definitions—and can
really be used interchangeably.
But to me there is a slight difference. “By foot” seems to mean using feet
as a mode of transportation, in the same way that you’d say “Going to the
store by car.” While “on foot” is more like the act of walking in the same
way you’d say “driving.”
So, you might say something like “How long does it take you to get there by
foot?” (using feet as a your mode of transportation) while you’d say “I’m
going to the store on foot” (meaning the act of walking).
A subtle distinction, and, as I said, basically interchangeable.
https://reurl.cc/97gz0x
When we talk about walking, we can say you go on foot or by foot, as a mode
of transport. Which preposition is correct? Technically, on is more accurate,
and common, and in exams you may be marked incorrect for using by foot.
https://englishlessonsbrighton.co.uk/say-on-foot-by-foot/
So which is more correct?
You move with your feet in contact with the ground, supported by your feet,
making on foot a more literal description of the action. Yet your feet are
also a tool of sorts, so if we want to describe what you use to travel, by
foot makes perfect sense. It is not reasonable, then, to say one is more
correct than the other. Yet you may be told that by foot is incorrect. Why?
For the same reason that many rules exist in English:
Because on foot is more commonly used than by foot.