Boltar wrote:
This morning I saw a black cab do a u-turn on a busy 4 lane road. And
not for the first time.

Doing a U-turn is a legal manoeuvre, unless there is a no-U-turn sign.
Unlike most drivers, taxis do not know where they are going to go when
they start their journey.

As long as the taxi did his U-turn in a safe manner I can't see why he
shouldn't.

Previously I've seen them stop suddenly in a red route to pick up a fare,
sometimes blocking the road,

Taxis are allowed to stop in red routes to pick up a fare. Obviously
they shouldn't "stop suddenly" but my guess is that he indicated then
slowed down and stopped. Perhaps you weren't watching properly or were
tailgaiting.

cut up other drivers, jump red lights and almost run down some pedestrians.

True that those are not permitted.