Somewhere between the Tube and the Taxi is the Heathrow express to Paddington, which is about a 15 minute trip, and is much easy to get to street level and taxis than the tube. There is even first class, which may or may not have porters to deal with bags. i’ve heard a cab from heathrow can be a fortune and a long ordeal.
http://www.heathrowexpress.com
For Gatwick
gatwick to victoria:
http://www.gatwickexpress.com