In Nottingham a fair number of signs say "where Taxi means Wheelchair Accessible Taxi"...legally there's two distinct things that are lumped together as "taxis" in common usage- Hackney Carriages and Private Hire. The latter are often referred to as Minicabs.
Hackney Carriages are those that you can hail at the kerbside and that can use taxi ranks. Private Hire are those that must be booked by phone or app. Uber in this country operate using Private Hire licences.
London is more regulated than other places- all the Hackney Carriages have to be of specific models, those operating in the central area have additional qualification requirements. Crucially though in London only Hackney Carriages count as "taxis" when it comes to Bus Lanes. TfL have been challenged on this by Addison Lee in court and won. In the rest of the country, this seems to not be the case, and Private Hire can use buslanes.
I've noticed a significant number of (normally appalling driven) private hire vehicles are on Wolverhampton Plates - presumably their licencing is pretty lax compared with the authorities in the Nottingham area. There's also quite a few doing the rounds in the city with Gedling plates - seems like they are a favourite as they have "For Hire" boxes on the roof, presumably as they double up as Taxi's in Gedling borough itself?