We're in the Departures area of the Heathrow airport. Fortunately, the Left Luggage place had the box they set aside for me, and their shipment of 10 bicycle boxes came in. Thanks to our persistance, Terminal 3 Arrivals Left Luggage/Excess Baggage now has 9 bicycle boxes in stock for the next 9 cyclists who decide to cycle to the airport to catch their flight out.
We tried out the tunnel to Terminals 1 and 3 today rather than cycling all the way to Terminal 5 and then catching the Express back to Terminal 3. When you follow the pink cycling path into Terminals 1 and 3, the path takes you to Terminal 1. From there, you walk down a ramp and through the underground hallways to Terminal 3.
I will put all this information together on my journal for future reference.