Heathrow asked airlines to cut 10% of flights at two terminals on Monday while easyJet started cancelling thousands of summer flights.
The move by Heathrow affected around 5,000 passengers at Terminals 2 and 3 on approximately 30 flights.
It comes after images emerged on Friday of a huge pile-up of passengers’ luggage.
A spokeswoman for Heathrow said: “We apologise unreservedly for the disruption passengers have faced over the course of this weekend.
“The technical issues affecting baggage systems have led to us making the decision to request airlines operating in Terminals 2 and 3 to consolidate their schedules on Monday June 20.
“This will enable us to minimise ongoing impact and we ask that all passengers check with their airlines for the latest information.”
EasyJet announced it is cancelling summer flights in a bid to avoid last-minute cancellations and in response to caps introduced by Gatwick and Amsterdam Schiphol airports.
It said it is “proactively consolidating a number of flights across affected airports”.
The aviation sector across Europe is experiencing “operational issues” including air traffic control delays, staff shortages in ground handling and at airports, and increased times for identity checks of new recruits, easyJet said.
The airline has cancelled thousands of flights in recent months, particularly during school holidays at Easter and the half-term period, which coincided with the Jubilee bank holiday weekend.
Chief executive Johan Lundgren told reporters “I can’t tell you how many flights will be impacted” as “we need to work this through”.
He added: “It would be misleading for me to give any numbers today because we simply don’t know.”
Mr Lundgren said easyJet had previously planned to operate around 160,000 flights between July and September.
In May, the carrier expected its capacity to be at around 97% of 2019 levels over that three-month period, but this has been reduced to 90%.
EasyJet admitted there will be a “cost impact” from the disruption, and the amount of money it spends to operate each seat per kilometre excluding fuel will “exceed” previous guidance.
It said: “We believe that these capacity/cost impacts are a one-off this summer as we would expect all parties to build greater resilience in time for 2023 peak periods.”
Mr Lundgren said: “Delivering a safe and reliable operation for our customers in this challenging environment is easyJet’s highest priority and we are sorry that for some customers we have not been able to deliver the service they have come to expect from us.
“While in recent weeks the action we have taken to build in further resilience has seen us continue to operate up to 1,700 flights and carry up to a quarter of a million customers a day, the ongoing challenging operating environment has unfortunately continued to have an impact, which has resulted in cancellations.
“Coupled with airport caps, we are taking pre-emptive actions to increase resilience over the balance of summer, including a range of further flight consolidations in the affected airports, giving advance notice to customers, and we expect the vast majority to be rebooked on alternative flights within 24 hours.
“We believe this is the right action for us to take so we can deliver for all of our customers over the peak summer period in this challenging environment.”
Mr Lundgren disputed the Government’s insistence that Brexit is not having a major impact on staff shortages in the UK’s aviation sector.
He said: “I do disagree with that because you can just look at some of our staff.
“We turned down 8,000 applicants from the EU.
“If you’re looking pre-pandemic, we would have been turning down probably around two to two-and-a-half per cent of people for nationality reasons because you would need to have a visa.
“That number for us is about 35 to 40%.
“The pool is smaller. That’s just fact, it’s just numbers.”
Ryanair, which has been largely unaffected by recent cancellations, announced it has added 200 “rescue flights” on its routes serving 19 UK airports until the end of September.
This is aimed at passengers whose flights have been cancelled by easyJet, British Airways and Tui, the Dublin-based carrier said.