on foot

From Middle English on fote, from Old English on fōte (“on foot”), equivalent to on +‎ foot.

on foot

1. On one's feet; walking, jogging or running but not in a vehicle or on the back of an animal. [from 10th c.]

   The pub's not far: let's go on foot.

2. (now rare, chiefly hunting) On the move; astir. [from 14th c.]
3. In progress or in preparation; active, in operation. [from 16th c.]
   • 1789, John Moore, Zeluco, Valancourt 2008, p. 113:

     [W]ithin a short time it was generally believed at Naples, that a treaty of marriage was on foot between Zeluco and the young lady in question […] .

• (walking, jogging or running): by foot, afoot