"Charles Ellson" wrote
It [Bristol] was previously (pre-*von) "City and County of" but IMU no
local
authority devoid of subsidiary authorities is currently classified as
a "county" for local government purposes, although other bits of
officialdom or semi-officialdom might continue to do so.

Clive Feather pointed out in an earlier thread that some (all?) unitary
authorities are defined as counties in the statutory instruments covering
their creation, but I think you are correct if you mean that they are not
regarded as counties by most people - except perhaps for one or two special
cases (like Bristol?) Conversely, some counties (e.g. the metropolitan
counties) seem to exist even though they have no council.