A lot of people appear to have started using the phrase “the man on the Clapham omnibus” recently. Unfortunately most people are using it as a slightly pretentious way of referring to the man on the street.
The man on the street, being the average man, is a mere statistical unit of public opinion. He is subjectivity personified.
To use the good fellow on the Clapham omnibus in that context is to misunderstand the thought experiment that is intended. The man on the Clapham omnibus is essentially a hypothetical independent reasonable person.
This means that he displays no bias and no judgement without reason. He is as objective as a man may be.
The two are polar opposites.