There are several apps for hailing black cabs. There are also services where you can phone to order a black cab that have existed since before that:

https://tfl.gov.uk/modes/taxis-and-minicabs/book-a-taxi?intc...

There isn't a central service that gives you access to all cabs, though.

TfL used to have a service where you could text them, and they would text back two phone numbers for local minicab firms near you. That was really useful for getting home when you were in an unfamiliar part of town.