I don't think you need any special licence to drive a taxi.
To drive a black cab is a different matter though.
Certainly in London you have to have the "knowledge", which is a test that proves you know the roads.
This probably applies all over the country, at a guess.
Also, my understanding is that black cabs or TOA (Taxi Owners Association, I think) is a closed shop and very much a "dead man's shoes" job, ie you have no hope until someone dies and even then, there's a massive waiting list.
My son-in-law was a taxi driver for a private taxi firm, so this is what I'm basing my answer on.
He told me it's a rubbish job, FWIW
As I said, it comes from what my SIL has told me, so I'm happy to be corrected