A total of 387 people were arrested between February 2016 and February 2017 - up from 255 the previous year.
Meanwhile more than half of cabin crew who responded to a survey said they had witnessed disruptive drunken passenger behaviour at UK airports.
The Home Office is "considering" calls for tougher rules on alcohol.
The arrest figures obtained by Panorama came from 18 out of the 20 police forces with a major airport in their area.
Trade body Airlines UK said it should be made illegal for people to drink their own alcohol on board a plane.
A total of 19,000 of the Unite union's cabin crew members were surveyed and 4,000 responded, with one in five saying they had suffered physical abuse.
A former cabin crew manager with Virgin, Ally Murphy, quit her job last October after 14 years and told Panorama: "People just see us as barmaids in the sky.
"They would touch your breasts, or they'd touch your bum or your legs. I've had hands going up my skirt before."
In July 2016 the aviation industry introduced a voluntary code of conduct on disruptive passengers, which most of the big airlines and airports signed up to.
The code's advice included asking retailers to warn passengers not to consume duty-free purchases on the plane, while staff are also asked not to sell alcohol to passengers who appear drunk.
Panorama found more than a quarter of cabin crew surveyed were unaware of the code of practice and, of those who had heard of it, only 23% thought it was working.
One anonymous crew member told Panorama: "The code of conduct isn't working… We're seeing these incidents on a daily, a weekly, a monthly basis. It's the alcohol mainly in the duty free that is the significant problem."
Sources: Airlines UK* and UK Travel Retail Forum**
Manchester Airport is one of the signatories but when Panorama's undercover reporter asked at World Duty Free whether she could open alcohol bought at a duty-free shop to consume on the plane, she was told "officially probably not, unofficially I think you'll get away with it". Another shop in the airport did give the right advice.
World Duty Free said it was committed to dealing with the issue and that it displays "clear advisory notices at till points, on till receipts and on carrier bags that remind customers that alcohol purchases cannot be opened until their final destination is reached".
Airlines UK, which represents carriers such as Virgin, British Airways and EasyJet, wants the government to amend the law to make consumption of a passenger's own alcohol on board an aircraft a criminal offence.
Airlines can limit the amount of alcohol sold to passengers on board flights.
Low-cost airline Jet2 has already banned alcohol sales on flights before 08:00 and managing director Phil Ward agreed further action was needed.
"I think they [airports] could do more. I think the retailers could do more as well.
"Two litre steins of beer in bars, mixes and miniatures in duty free shops, which can only be there for one reason - you know, they're items that are not sold on the high street.
"We can't allow it not to change."
A House of Lords committee report earlier this year called for tougher rules on the sale of alcohol at airports.
Committee chair Baroness McIntosh of Pickering said: "We didn't hear one shred of evidence to show the voluntary code was either working now or had any possible vestige of success in working any time soon."
The Home Office said it was considering the report's recommendations, which include revoking the airports' exemption from the Licensing Act, "and will respond in due course".
Karen Dee, chief executive of the Airport Operators Association, said: "I don't accept that the airports don't sell alcohol responsibly. The sale of alcohol per se is not a problem. It's the misuse of it and drinking to excess and then behaving badly."
She said they were working with retailers and staff to make sure they understand the rules.
Arrests of passengers suspected of being drunk at UK airports and on flights have risen by 50% in a year, a Panorama investigation has revealed.