In the for-what-it's-worth department, my pre-LEL destination is (at present) the Lee Valley Hostel in Cheshunt. Combinations of airport express trains, Underground, and Overground rail seem to work.
Flying from Seattle, Washington, on the upper left corner of the USA.
If I fly to Heathrow, I can take the Heathrow Express (really fast, costly) to Paddington, or Heathrow Connect, 1/2 to 1/3 as fast, and 1/2 the cost, also to Paddington. Two different Underground lines, both bike-permitting (though my bike will be in a padded bag at the time, thus "luggage") go to Liverpool Street Station, where I can take the Overground to Cheshunt.
If I fly to Gatwick, I can take the Gatwick Express to Victoria station, and then either of the same two Underground lines around to Liverpool Street, and then the Overground, etc.
For flights from or to western North America, Heathrow and Gatwick seem to be the "only" airports -- at least for airlines which I can fly using frequent flyer miles, and which also have at most one stopover.