Walk on foot or walk by foot?

Although the expression 'going on foot' is more often used, 'going by foot' is equally correct.

Comparing the usage of 'on' and 'by', most people would say they are going by car, by train, by air, etc., when traveling, not on car, on train, or on air. If riding a bicycle, it would be correct to say you are going by bicycle, not going on bicycle.