Car hire can work but it's often more expensive, needs to be booked ahead of time and they also refuse trips that aren't profitable for them.
Uber openen up travel for many people in London, especially at night. It's quite easy to find a lot of places in London that aren't serviced by Night Buses, there are plenty of places that are 15-30 min walk from a tube station, and the Night Tube is only available on select lines and only during the weekend.
They're bad in the center too. I live in London bridge / SE1 and black cabs still illegally refuse to take me home from say, Shoreditch because they can't be bothered crossing the river.
I don't know if they still do, but many nightclubs would have some arrangement where there was someone from a minicab company in the lobby or just outside. You'd say "W3", he'd say "That'll be £20, in 10 minutes time" and you could wait in the warm until the car arrived. (Of course, if you knew a number for a different company, you could phone them yourself.)
The drivers were pretty clueless -- even a fairly large inner-London station name like "Ealing Broadway" would frequently be misunderstood, and they'd want to slowly type a postcode into a satnav -- but otherwise they were OK.
