Anybody that does frequent business in London knows all about how much of a headache it can be to make it from London to Heathrow in a timely manner, particularly to the international airport there. This is especially true during peak hours of the day. As one of the most prominent gateways between London and the rest of the world, it's no surprise that the route between the inner city and Heathrow would experience some traffic flow issues from time to time.
If you're obligated to make this voyage on a regular basis, you've got a few viable options. Almost all of them require a little bit of planning ahead in order to remain within the parameters of any sort of reasonable itinerary you may have had in mind, but some require a lot less than others. The distance between these two cities, geographically speaking, is not that far. Still, as short of a commute as it is, one would think that the train system that runs back and forth amidst these two destinations would be the best option. You don't have to deal with road traffic, after all, and it's fairly inexpensive.
But no, that's simply not the case. Taking taxis to Heathrow is by far the best option if you're traveling from London. The taxi cab drivers that frequent that route know how the traffic flows throughout different parts of the day very well, and are more likely to be able to get you to your destination without a significant delay.
Trains, on the other hand, get delayed all the time. They can't reroute that easily if there's a problem, whereas a car can simply find an alternate roadway to take. Who who knows multiple routes to take to the same destination better than a taxi driver that's probably driven those roadways hundreds upon hundreds of times.
When it all boils down, taking taxis to Heathrow instead of getting there any other way makes far more sense. Even if it costs a bit more to pay for taxi fares than for alternate transportation, the convenience of not having to contend with train schedules and other sources of turmoil makes it more than worthwhile. Try it both ways in the course of your commuting, and see if you don't agree.