The rail link is proving so popular that at peak periods of the day there is not enough time to collect all the fares before the train reaches its destination.
BAA, the airports group that owns the link, plans to tackle the loss of revenue by increasing the number of staff selling tickets before the trains depart.
The service is being marketed under the slogan "Famous for 15 minutes" because the trains run four times an hour between Heathrow and Paddington station and the journey takes a quarter of an hour.
BAA deliberately decided to allow passengers to buy tickets on board to avoid delaying them at either end of the journey.
Sir John Egan, the chief executive of BAA, was recently complimented on the service by the wife of an ambassador to Britain who said: "So wonderfully fast and all for free as well."
The pounds 450m link is on course to transport 15,000 passengers a day this year - 12 per cent of all those using Heathrow - reducing the number of road journeys to the airport by 3,000 a day.
Although there was initial criticism of the pounds 10 single fare, there have been very few complaints about the pricing and BAA is considering increasing its charges.
From 2001 it expects to start operating a sister service from St Pancras station to Heathrow, which will take 35 minutes. It is also planning to redevelop Hayes station in west London to increase the number of BAA staff travelling to Heathrow by train.
The Heathrow Express will eventually link up with Terminal 5 provided BAA gets the go-ahead. The inspector's report is due to be presented to the Government in 18 months, rather than the two years it was originally expected to take.