Oil is the single biggest element of an airline’s cost base, Mr Walsh said during an interview with the BBC Sunday Morning programme.
Flying will be more expensive for consumers, “without doubt”, he said.
“It’s inevitable that, ultimately, the high oil prices will be passed through to consumers in higher ticket prices,” Mr Walsh added.
Surging oil and gas prices, exacerbated by Russia’s military offensive in Ukraine and increased demand from economies recovering from the Covid-19 pandemic, have fed into rising global inflation.
Brent, the benchmark for more than two thirds of the world’s crude, rose to a notch under $140 a barrel in March. It has given up some gains since then, but is still trading around the $105 mark.
Inflation globally has risen sharply amid a steep rise in the prices of food and other commodities since the Ukraine conflict began in February.
Inflation is this year forecast to reach 5.7 per cent in advanced economies and 8.7 per cent in emerging markets and developing economies, according to the International Monetary Fund.
Among the many negative effects of an escalation of the Russia-Ukraine war on aviation, rising fuel costs and dampened demand owing to lowered consumer sentiment would be paramount, Iata said during its annual general meeting in Doha last month.
Fixing battered balance sheets carrying $650 billion in debt would be another major challenge for airlines this year, the industry body said.
Airlines are expected to post $9.7bn in collective losses this year, a sharp improvement from about $42bn in losses in 2021, Mr Walsh said in Doha.
Holidaymakers need to be prepared for the cost of flights to go up, Mr Walsh told the BBC.
Many of the issues affecting airlines and airports were caused by staffing problems in the wake of Covid. However, Mr Walsh said he had “no regrets” about making deep cuts to British Airways’ headcount during the pandemic, when he was running the airline.
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“People are flying in ever greater numbers. It is a time for optimism, even if there are still challenges on costs, particularly fuel, and some lingering restrictions in a few key markets,” he said during the Iata meeting in Doha.
Aviation was among the industries hardest-hit by the pandemic, which had a domino effect on tourism, hospitality and supply chains. However, the sector is making a gradual recovery.
While the underlying demand for travel is strong, there is a downside risk should governments choose to return to knee-jerk, border-closing responses to future outbreaks, according to Iata.
“Governments must have learnt their lessons from the Covid-19 crisis. Border closures create economic pain but deliver little in terms of controlling the spread of the virus,” Mr Walsh said.
“With high levels of population immunity, advanced treatment methods and surveillance procedures, the risks of Covid-19 can be managed.”