Uber are trying to be two different things
In the UK at least we have two different forms of taxi. We have the Hackney Carriage which holds is own operator's licence and is allowed to take bookings on the street. These are very strongly regulated, must be wheelchair accessible and are able to charge fares based on distance and time.
On the other side you have the private hire sector, these are generally a lot less regulated than the Hackneys, the operator's licence is held by the taxi company and bookings can only be made with the operator, so the cars can't pick up off the road. Importantly they can only charge by distance.
Both of the above have regulated fares. Hackney fares are set by the Local Authority and private hire have to submit their fare sheets for approval too.
Uber attempts to circumvent this in a number of ways. There is nothing stopping Uber setting up as a private hire company in the UK, however their pricing models are not compatible with the way taxi licencing is done in a lot of the UK. Private hire companies can't just put a surcharge on because their busy (Surge pricing is one of Uber's defining characteristics), they also can only charge by the mile, whereas Uber's app charges you for both time and distance travelled.
Uber are trying to straddle the line between being a black cab and being a private hire, while adding some extras in that aren't strictly legal either.