Passengers have complained of queues and "total chaos" at Heathrow after the airport asked airlines to remove 30 flights from Thursday's schedule.
The UK's largest airport asked airlines to cut the flights because it was expecting more passenger numbers than it can currently cope with.
Some passengers did not know that their flights were cancelled until they arrived at the airport.
Heathrow said the cancellations were necessary for safety.
Travel writer and broadcaster Andy Mossack tweeted that there was "total chaos" and "zero customer service" at the airport on Thursday morning.
Mr Mossack, who was due to fly to Geneva at 08:25am, told the BBC he was told of the cancellation via an email about 6.00am which he didn't see until he arrived at the airport.
"There are no flights to Geneva until Sunday or Monday. So I've had to come home".
Terminal 5 was "awful... there were hundreds of people there. Some sleeping on the floor".
Another passenger tweeted that terminal 5 was a "disgraceful shambles" after he arrived on Thursday morning to find his flight cancelled.
PA reported that one passenger, Andrew Douglas, said he had spent four hours in queues to find out at check-in that his flight had been cancelled with no prior notifications.
Other travellers complained of poor customer service and a lack of help when trying to rebook their flights.
A Heathrow spokesman said: "We will work with airlines to get affected passengers rebooked onto other flights outside of the peak so that as many as possible can get away, and we apologise for the impact this has on travel plans.
"We are working hard to ensure everyone has a smooth journey through Heathrow this summer, and the most important thing is to make sure that all service providers at the airport have enough resources to meet demand."
A spokesman from British Airways, one of the airlines affected, said: "As a result of Heathrow's requirement for all airlines to reduce their schedules, we've made a small number of cancellations."
The airline said it was in contact with affected customers to "apologise, advise them of their consumer rights and offer them alternative options, including a refund or rebooking."
Virgin Atlantic said one of their Heathrow to New York return services had been cut in each direction, while Air France, KLM, American Airlines, Delta Airlines, Lufthansa, Aer Lingus, Brussels Airlines and Air Canada are also affected.
Meanwhile, the government is calling on the industry to run "realistic" summer schedules and alert passengers to any flight changes as "early as possible" to minimise disruption.
"It's now on airports and airlines to commit to running the flights they've promised or cancel them with plenty of time to spare so we can avoid the kind of scenes we saw at Easter and half term," said Transport Secretary Grant Shapps.
Among the 22 measures the Department for Transport introduced on Thursday is a plan to give airlines a short window to hand back plane parking slots for the rest of the summer season.
This is aimed to help manage capacity at the busiest airports.
Earlier this month, around 5,000 people were hit by Heathrow cancellations because of technical issues affecting baggage.
Before that, tens of thousands of passengers had been affected by disruption at UK airports and flight cancellations during the week of the Platinum Jubilee and half-term holidays.
The disruption was caused by several factors, but staff shortages have left the aviation industry struggling to cope with resurgent demand.
Last week when Heathrow made a similar move, it was for a different reason - because of the knock-on impact of a technical problem with baggage.
This time, it's linked to staffing; it realised more passengers were going to come through the airport the next morning than it has capacity for right now.
But why was the decision only announced on the afternoon of the day before?
The airport says it's seeing increasing numbers of last-minute bookings following cancellations or disruption at other airports - and this is pushing up passenger demand. Thirteen percent more passengers were booked to fly today than Thursday last week.
Heathrow says it's constantly talking to airlines, working with them to make sure the right amount of airline, airport and ground handling resources are in place to cope with the number of flights operating.
Gatwick has already announced it's limiting flight numbers for July and August. Heathrow hasn't done that, but points out that since Gatwick's announcement, the government has announced a one-off "amnesty" on airport slot rules, and airlines are expected to use this to cut more flights to try to make schedules more resilient.