The Underground link to Britain’s busiest airport is supposed to run every five minutes, with half the trains serving Terminal 4 and half Terminal 5. All trains serve Heathrow Central, location for Terminals 2 and 3.

But even at the height of rush hour, gaps have extended to 15 minutes between trains to Britain’s busiest airport — with longer waits still for passengers at Heathrow Terminal 5. Trains are so full that some passengers, particularly those with luggage, are unable to board at central London stations.

A series of issues including leaf fall, water on the tracks and the current cold snap has triggered problems with adhesion between the wheels and the rails. This has led to a large number of “wheel flats”. Trains, many of which are 40 years old, have to be taken out of service to be repaired.

Tony Matthews, general manager for the Piccadilly line, said: "We do not have a full fleet available to run a good service. We will continue working around the clock to repair the wheels so that we can return to giving our customers the high level of service that they deserve as quickly as possible."

The RMT union, which represents many Tube workers, has called for “serious consideration to the Piccadilly line being closed” while trains are fixed, warning that the line is “inherently unsafe”.

The union’s general secretary, Mick Cash, said: "The entire Piccadilly line fleet of trains has got a major engineering problem which has finally boiled over. It's nothing new and it is down to pressure on services and sheer managerial incompetence.”

Passengers to and from the airport can also use the Heathrow Express and Heathrow Connect rail services, but these are much more expensive. Passengers paying with a contactless card pay a maximum of £5.10 for a peak-hour Piccadilly line train. The Heathrow Connect fare is twice as much, at £10.20, while the Heathrow Express is £22.