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Declining consumer confidence could see demand for holiday flights fall and a tough outlook for Britain's companies could bite into demand for business travel.
Both men have also faced heavy criticism from customer groups over the botched opening of Terminal 5. They have both publicly apologised for the fiasco.
"We made mistakes and we let people down. Though the mistakes were by no means the sole preserve of BA, we held our hands up, we took responsibility and we apologised," Mr Walsh told investors.
Mr Walsh turned down an bonus worth up to £1.4 million in the wake of the Terminal 5 chaos, describing the payout as "inappropriate" in the circumstances.
One leading institutional shareholder in BA said that this had "taken a lot of the heat" out of today's annual meeting.
There were bound to be discussions between BA and its owners about ironing out the teething troubles at Terminal 5 and the issue of high fuel costs, the shareholder said. But these were general, long term issues rather than immediately urgent worries, he said.
Despite the bonus pledge, Mr Walsh still received a 5 per cent increase in his annual base salary to £735,000. He could receive a bonus worth more than £1 million for the current financial year if performance targets are met.
Another City fund manager and BA shareholder said that while he was broadly supportive of the airline's strategy the airline is not really in control of its own destiny.
"The big danger is that it is not in their hands - it's all in the oil price," he said.
"The way they are operating is actually quite sensible. They are hunkering down to see whether all of the current pain will result in some capacity coming out of the market.
"But it's very tough. They can't control the price of fuel. The consumer outlook is weaker; the corporate outlook is weaker. I don't see them making much money this year."
The sharp increase in fuel prices has prompted a rash of fuel tax increases by the airline, further incurring the ire of customers.
A spokesman for BA said Mr Broughton's comments did not amount to a profits warning. "It's not a profits warning, it's an outlook," he said.
BA said at its annual results in mid-May that the environment was challenging, he said.
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