I'm aware that private hire taxi licences are "portable " - get your licence in, say, Bristol, and it will allow you to work in, say Blackpool ( or wherever).
Round here if the licence isn't from the (truly) local authority, then all I see is private hire cabs with "City of Wolverhampton " plates.
Why just Wolverhampton? Is the Wolverhampton licence easier or cheaper to get ? There must be some reason as to why.