Bristol was not unique: Newcastle upon Tyne was also independent of the two adjacent counties. It was a City Borough, although standing north of the River Tyne and (you'd have thought) part of Northumberland.

I suspect that quite a lot of English cities fell into the same category, having a status and a pride that made them different from the surrounding country and requiring a different governance.

Backing this, "county" types are well-to-do individuals who live in the country. People who live in the cities and towns outside of London are simply provincials.