Mostly in London, you used minicabs because the Black Cabs were soooo expensive, and they had all these different fare modes depending on what time of day or night it was, and they'd tick at different rates depending how fast they're going and all sort of other black-box opaque bullshit.

At the end of a night outside clubs, there'd be (illegal) minicabs everywhere, offering to take you wherever for much less than a black cab, and sometimes that's just all the money you have left. Usually they'd get lost or be terrible in some other way very well-described above.