No, but you do have city managed taxi drivers where the city limits how many licenses are given out. While they aren't transferrable like the US medallions, that doesn't change the point of the post.
Not in London (which is mostly where Uber works) and the number of private hire licences (again, the category which Uber operates in) are not IIRC limited anywhere. And in practice the value of a taxi over a private hire licence not much higher anywhere except London because there's much less street hailing and a car is only a phonecall (or app click) away.
