Emirates has rejected an order from Heathrow to cancel flights to comply with a cap on passenger numbers.
The airline accused the west London airport of showing “blatant disregard for consumers” by attempting to force it to “deny seats to tens of thousands of travellers”.
Virgin Atlantic also criticised Heathrow’s actions and claimed it was responsible for failures which are contributing to the chaos.
On Tuesday, the UK’s busiest airport introduced a cap of 100,000 daily departing passengers until September 11, and pleaded with carriers to stop selling summer tickets.
Emirates plans to operate as scheduled— Emirates
Many passengers flying to and from Heathrow have suffered severe disruption in recent months, with long security queues and baggage system breakdowns.
Emirates, which operates six daily return flights between the airport and Dubai, said in a statement: “LHR (London Heathrow) last evening gave us 36 hours to comply with capacity cuts, of a figure that appears to be plucked from thin air.
“Their communications not only dictated the specific flights on which we should throw out paying passengers, but also threatened legal action for non-compliance.
“This is entirely unreasonable and unacceptable, and we reject these demands.”
It added: “Until further notice, Emirates plans to operate as scheduled to and from LHR.”
Faced with an 'airmageddon' situation due to their incompetence and non-action, they (LHR) are pushing entire burden - of costs and the scramble to sort the mess - to airlines and travellers— Emirates
The Gulf carrier said its ground handlers at Heathrow are “fully ready and capable of handling our flights”, which means “the crux of the issue lies with the central services and systems which are the responsibility of the airport operator”.
It stated it would be “impossible” to re-book the number of passengers that would be affected by Heathrow’s cancellation demands.
Moving some of its operations to other UK airports at short notice is also “not realistic” as locating somewhere that can facilitate a widebody long-haul aircraft carrying 500 passengers is “not as simple as finding a parking spot at a mall”, the airline explained.
The statement added: “The bottom line is, the LHR management team are cavalier about travellers and their airline customers.
“All the signals of a strong travel rebound were there, and for months, Emirates has been publicly vocal about the matter.
“We planned ahead to get to a state of readiness to serve customers and travel demand, including rehiring and training 1,000 A380 pilots in the past year.
“LHR chose not to act, not to plan, not invest. Now faced with an ‘airmageddon’ situation due to their incompetence and non-action, they are pushing entire burden – of costs and the scramble to sort the mess – to airlines and travellers.
“The shareholders of London Heathrow should scrutinise the decisions of the LHR management team.”
Virgin Atlantic chief customer and operating officer Corneel Koster called for a “measured approach” to tackling disruption which balances the need for Heathrow to be more resilient with the impact of stopping people who “really want to travel” from boarding flights.
In an interview with PA News, he said: “We’re quite concerned that what they’re doing is not targeted enough.
“It should be focused on ‘what are the bottlenecks, how are we mitigating those temporarily, and how are we really getting beyond this?’.
“We expect them to show us the plan of how we’re going to get back to 2019 capacity.
“We haven’t seen enough of a plan.”
He added: “We can’t give up on summer.”
In December last year, Heathrow said it expected passenger numbers for 2022 to reach around 45 million.
It subsequently raised its forecast to “nearly 53 million” in May, and 54.4 million in June.
Terminal 4 was only reopened on June 14, some three months after the UK lifted all remaining coronavirus travel restrictions.
It was the last terminal at a major European airport to resume operations during the pandemic.
Mr Koster said: “Everybody should have got ready for this increased demand.
“If you’re around the table and the Heathrow voice says ‘it won’t happen, it will come later, I will only open my fourth terminal in June’, that’s a planning mistake.
“They have downplayed demand. They should have opened T4 earlier.
“They should have played an even stronger role in the community.”