LONDON (Reuters) - A no-deal Brexit could wreak chaos for travellers and a nightmare at airports, global airline industry body IATA warned, calling on British and European Union aviation authorities to put in place a plan to avoid such a worst-case scenario.

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Britain is set to leave the European Union on March 29, 2019 but with just over five months to go, Prime Minister Theresa May has yet to reach a withdrawal deal and both sides have stepped up preparations for the possibility there will not be one.

The International Air Transport Association (IATA) said on Wednesday that planning for a no-deal Brexit needed to move much faster to ensure planes can keep flying and safety and regulatory frameworks keep functioning whatever the new relationship between the pair after March 29.

“We predict chaos if nothing is done,” IATA Director General Alexandre de Juniac told reporters on a call on Wednesday.

“On April 1 it will be us, the airlines, who have to manage millions of passengers potentially grounded in airports unable to take a flight ... It will be a nightmare in European airports and UK airports,” he warned.

Separately, IATA released forecasts on Wednesday showing that airline passenger numbers could double to 8.2 billion in 2037, bolstered by strong demand in Asia, though protectionism risks curtailing growth.

De Juniac said the trend towards restricting free trade, such as the introduction of recent tariffs, was weighing on the aviation industry’s most recent forecast of 3.5 percent compound annual passenger growth rate over 20 years, down 0.1 percent from an earlier report. That small decline means 60 million fewer passengers over 20 years.

On Brexit, de Juniac said that airlines were “completely in the dark” as to how to plan for what sort of flying rights, safety framework and border management would exist if there is no deal due to a lack of transparency around the discussions. He said they needed certainty on these three critical issues.

Flying rights to, from and within the EU, as well as between the United States and Britain, are covered by EU-wide “Open Skies” agreements. But unlike with trade, where Britain would revert to World Trade Organization rules under a no-deal, there is no default fallback option for the aviation sector.

“A backstop contingency plan to keep planes flying after March must be published, and quickly,” de Juniac said.

The exclusion of the airline industry from EU-British discussions was exacerbating the potential for chaos, he warned, adding that IATA was ready to offer solutions if asked.

The chief executive of Ryanair RYA.I, one of Europe's biggest airlines, has warned that if there is a no-deal Brexit, UK flights could be grounded for up to three weeks.

IATA said it did not expect a scenario where all flights were grounded. “As a short term, emergency fall-back position, we understand that the EU and UK CAA have plans for a ‘bare bones’ agreement ... to ensure at least a basic level of connectivity,” IATA said in a study also published on Wednesday.

But it warned that minimum connectivity could be as little as 5 percent of the current number of weekly flights between Britain and Spain.

In Montreal, Airbus SE AIR.PA planemaking head Guillaume Faury told reporters on Wednesday the European company is working on priorities if there is no deal.

“For the moment our focus is completely on managing the transition period and making sure there is no disruption,” he said,” he said. “This uncertainty is by the way, one of the most difficult stakes (involving Brexit).”