Virgin Atlantic is withholding the fees it pays to airport operator BAA because of the "slow reaction" to December's heavy snow.
The airline says it will not pay any airport fees until the results of the full inquiry into the poor reaction to the snow, which are due at the end of March.
Heathrow and other airports temporarily closed during heavy snow in December, affecting many thousands of passengers and costing the industry millions.
The inquiry was launched just before Christmas, looking at "what went wrong" at Heathrow, where flights were grounded for days.
Virgin is one of BAA's biggest customers. Along with other airlines, is has been critical of the length of time it took to clear plans for take-off following the disruption.
BAA said that Heathrow's conditions of use provided no basis to withhold charges.