In London minicabs and black cabs are very different. Black cabs can be hailed whereas minicabs have to be booked and are regulated differently.
They are not rare in city centres, which is their natural habitat eg. take a trip into Central London/Westend/City of London etc., you will find them everywhere. Unless, you are talking about the suburbs, where they have always been as rare as hens teeth.
https://tfl.gov.uk/info-for/taxis-and-private-hire/licensing...