michael,
you'll struggle to get a minicab at Heathrow unless you've pre-booked one as the airport police seem to spend more time chasing off taxi-touts than anything else. I believe that a cab from here (I'm about 3 miles from Crowthorne) to the airport would set you back about £35 - 40.
also, i'm fairly sure that you don't have to change at Wokingham. The Reading - Gatwick trains have two separate services - one stops at Crowthorne and the other doesn't.