Officials say 29-year-old Olesen -- who placed 6th at the 2013 Masters -- was a drunken menace on his flight from Nashville to London ... screaming at passengers and acting like a moron.

The most serious allegation is the alleged molestation of a female passenger. The details surrounding that particular incident is unclear.

During the hellish flight, a witness told The Sun ... Olesen began urinating right in the aisle of the 1st class cabin.

Olesen was traveling with fellow PGA star Ian Poulter -- the two had competed in the WGC-FedEx St. Jude Invitational in Memphis over the weekend.

Poulter reportedly tried to diffuse the situation during the flight ... and when he felt Olesen was under control, he decided to take a nap.

But, when he woke up, Poulter's rep says the golfer learned about the wild allegations against his fellow golf pro. In other words, Poulter feels he doesn't deserve a single ounce of blame.

The Met. Police Dept. (the agency which took Olesen into custody in London) tells TMZ Sports Olesen was booked on several charges including "suspicion of sexual assault, being drunk on board an aircraft and failing to comply with the orders of cabin crew."

We also reached out to British Airways, which said, "Our customers and crews deserve to enjoy their flights, and not to suffer any form of abuse."

"This sort of behaviour (they used the "u") will not be tolerated, and the appropriate action will always be taken."

Olesen was eventually released from custody and the incident is currently under investigation.

For what it's worth ... Olesen finished 27th in the tournament over the weekend and tweeted, "Not much to say, other than I’m pretty disappointed with today’s performance!"

"Now for some time off and practice to get things right."