which taxi company in london is best for airport transfer?

Depends where you're going to / from

(There are several London airports)

Never use them, when there is excellent pubic transport available for next to nothing.

Post your adverts elsewhere.

In Most cases, the London Underground (Tube) is quicker and cheaper

took a Taxi from Lambeth to London Airport after 2 Hrs in traffic the Driver dropped me off at the Tube and in less than one Hour was at the Airport

Never heard of them, 

Only if you want to be overcharged.

Uber is best world wide other car taxies brands would vary in prices by popularity