I agree with the other posters. Stay off the roads, especially at that time of day. Both the Gatwick and Heathrow Express trains run regular as clockwork, and you the Circle Line trip from Victoria to Paddington is 16 minutes. I've done this plenty of times and it's by far the quickest way.

Is your luggage being transferred? The only downside of the tube is that it can be a bit of a hassle if you have big bags.