The airlines are taking flight cancellations into account, offering discounted fares and discounting flights as part of a wider pilot programme to boost profits.

They have also cut the number of flights that can be booked to about 200 per day.

“It’s a bit like a Christmas miracle,” said John McKeown, senior analyst at Euromonitor International.

“A lot of people were looking at the numbers and thinking, ‘well, if you can’t get a flight, where can you get one?'”

It is not clear how many British Airways passengers have been affected by the pilot, which began on July 4 and is continuing through August.

The airline said it would review its business and operations plan after the pilot is over, but would not say how many cancellations had been made.

Mr McKeever said: “It will be interesting to see how it plays out.

It will be a bit of a shocker, but I’m sure there will be some happy families, but there will also be some unhappy ones.”

The airline is also limiting flights to the UK, Ireland and the Republic of Ireland.

“This is about ensuring that the cost of travel is not going up, so there is no cost to the consumer,” a spokeswoman said.

“Our strategy to support the consumer will continue as we look at how to reduce costs and offer the best value for money.”

But Mr McLeish said it was likely the airline would have to cut flights for British Airways customers to Ireland and Italy, as well as other destinations such as Spain, to stay competitive.

“That would mean the price of tickets on those flights will go up,” he said.

The European Commission has been monitoring British Airways’s flight cancellation policies for months, and the commission said it had made a formal complaint to the airline about the pilot.