The word 'taxi' tends to be used (particularly outside London) to embrace two separate types of vehicle:
Firstly, there are true 'taxis' (which are sometimes referred to be the old name of 'hackney carriage'). In London (and in some other major cities, such as Sheffield), a car driven on a taxi licence will normally be a traditional black cab. Elsewhere in the country, taxi drivers use normal saloon cars. A (true) taxi must have a meter and must charge fares according to a scale laid down by the local council. They can accept pre-booked calls or they can pick people up in the street or from taxi ranks.
Secondly, there are 'private hire cars'. (In London, they're known as 'minicabs'. Elsewhere, they're generally just called 'taxis', even though they're driven on a separate type of licence). Drivers of private hire cars don't require a meter in their car and they aren't governed by any fixed scale of fees. (They can charge what they like). However, they're only allowed to pick up customers who've pre-booked the car. (The only exception is that they're allowed to accept customers who walk into their office). They can't pick up fares in the street and they can't use taxi ranks.
Drivers of both types of vehicles require a licence to operate. (They should have a licence plate attached to the rear of the vehicle. In many areas, drivers must have a separate notice in the car and/or wear an official badge). While the local authority will make relevant checks (e.g. with the Criminal Records Bureau) before granting a licence, neither licence requires the driver to prove his geographic knowledge of the area. (The only exception is the 'Knowledge', required by London taxi drivers).
Chris