Aer Lingus has cancelled two one-way flights from London Heathrow to Dublin and Shannon today due to capacity reduction at Heathrow.
The airline said it is awaiting further direction from Heathrow to understand the impact on its schedule in the coming weeks.
In a statement, it said it will try to minimise disruption caused to customers.
Heathrow Airport has imposed a capacity cap of 100,000 daily departing passengers until 11 September amid a lack of resources.
Separately, industrial action at Bordeaux Airport and Lyon Airport has also led to the cancellation of two return flights tomorrow and one return flight on Saturday.
Aer Lingus has apologised to affected customers and said its teams are working to re-accommodate those impacted as soon as possible.
The airline said plans were in place to deal with the increased demand for travel following the lifting of Covid-19 restrictions, but a significant spike in cases in recent weeks – as well as system pressures and ongoing issues at some airports – has created "considerable additional operational challenges".
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Emirates has rejected an order from Heathrow to cancel flights to comply with the 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".
It 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."
Additional reporting: PA
