Cost is only one, relatively small, part of Uber's USP in London. The general shittiness of Black Cab drivers about taking you anywhere close to the edges of zone 1 is the biggest issue for me. Night tube only runs on Fri/Sat nights so I literally couldn't get home from a late week night without Uber.

I wouldn't be surprised to see Uber riders blocking taxi ranks if Uber actually stopped operating, Black Cabs serve very few Londoners.

Edit: Not "literally couldn't get home", I would just have to spend over an hour on a night bus.