Position yourself so as to be walking ahead of them at the same speed. Now, subtly decelerate, thus obstructing their path.
The Target Walker will attempt to overtake you. At the precise point they are walking in parallel with you, re-accelerate to their speed, such that you are now walking in step with them.
The Target Walker will then decelerate -- do likewise.
AT NO POINT RECOGNIZE or ADDRESS the Target Walker.
Repeat as required, accelerating or decelerating to impair the Target Walker's overtaking.
Continue unitl the Target Walker eventually loses their temper and challenges you. Simply turn to face them and say "What?!?"
(Indeed, what have you done wrong?)
[From Manzine, Issue 4.]