You hear both. On foot is correct.

On foot" and "by foot" both mean to walk or to travel by walking. They are interchangeable and can be used to describe the mode of transportation a person is using. For example, you might say, "I traveled to the store on foot" or "I traveled to the store by foot." Both of these sentences mean that you walked to the store.

You can use either but "on foot" is more accurate and common. However, in this instance I would say "I walk to work".

Hi Irina :-) Both are correct (I hear both). The most natural sounding way to say this in informal "US English" is by using the word "walk" instead. For example, "I walk to work". I'm proud of you, Nicky

I tend to use "by foot" as preference and I feel like it rolls off my tongue easier. "I'm going to work by foot today, I should have my car soon!"