You can book a taxi via following methods:
Online: http://www.londonblack-cab.com/
Telephone: +44 795 680 8896
Yes, it's possible to pre-book a taxi with The London Black Cab Taxi Service, please contact the company.
The London Black Cab Taxi Service has both regular and air-conditioned taxis, please mention your preference at the time of booking.
Please contact the company on their helpline number to make any changes.
Generally drivers will meet the passengers at the arrivals on airport pick ups but do check with the company.