Pilots represented by the British Airline Pilots Association at British Airways have begun a two-day strike.
Tens of thousands of passengers have been told not to go to airports.
British Airways said most have made alternative arrangements.
Pilots walked out at midnight in a dispute over pay and conditions.
It is the first pilot strike in the history of the airline, which is celebrating its centenary this year.
Both the carrier and union have said they are willing to renew talks, while British prime minister, Boris Johnson, last week urged them to “sort out” their differences.
Nonetheless, the vast majority of British Airways flights taking off from the UK on Monday and Tuesday have been cancelled.
There was also a knock-on effect to flights on Sunday, because planes and pilots needed to be in position for prior and subsequent journeys.
Dozens of flights were cancelled, and further unforeseen cancellations could happen on Wednesday, the airline said.
Some 4,000 pilots will strike and almost all of the 1,600 flights that were due to fly will be grounded.
In a statement, British Airways said: “We understand the frustration and disruption Balpa’s strike action has caused you.
“After many months of trying to resolve the pay dispute, we are extremely sorry that it has come to this.
“Unfortunately, with no detail from Balpa on which pilots would strike, we had no way of predicting how many would come to work or which aircraft they are qualified to fly, so we had no option but to cancel nearly 100 per cent our flights.
“We remain ready and willing to return to talks with Balpa.”