FDF
Taxi world, I have no up to date info other than website. I believe you are correct re area. The oddity was/is that Red Ken kept the GLA area to London Boroughs, but Staines had a portion of the airport (and still does?), cargo and T5 land, so the boundaries moved.
TFL the collected cabs from the Met Police in the GLA power struggle.
The 3rd runway area may even extend into Berkshire and/or Bucks territory