You can book a taxi via following methods:
Online: http://www.bluearrowgatwick.co.uk/
Telephone: +44 173 776 5676
Yes, it's possible to pre-book a taxi with Blue Arrow Gatwick, please contact the company.
Blue Arrow Gatwick 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.