"I love Italy, in fact I'd actually like to live there. I've been to Tuscany's Monte Pulciano to hear the work of my composition teacher, Hans Werne Henze. They have a festival there every August. It's fantastic - the locals get involved and play music too."
His travels include spells in Sienna and Venice.
"Venice was remarkable. I went to see Stravinksy's grave on the island where all Venicians are buried. Apparently, when it gets full up, they just chuck out a few bodies - mostly the less famous."
And 1986 saw Mark-Anthony back in the country again, this time on a boat from Naples to Sicily.
"When we arrived in Palermo I went to the most fascinating place I've ever been; underground catacombs with mummified Italians. You could see their skin and hair, and the costumes they were wearing at the time."
All rather grizzly, but not surprising from the bad boy of classical music whose works deal with themes such as drug addiction and whose last CD was entitled Blood on the Floors.
One stamp that brings a smile to Mark-Anthony's face is Antigua where he went on a package holiday with his wife in 1992.
"When we arrived at this tacky hotel, there was a drinking tap saying "free drink" which turned out to be beer. There were piles of men lying around in Man United shirts.
"We then went on a "Jolly Roger" boat trip around the islands, with a bunch of Americans who'd all paid to do things like "walking the plank". And every evening, back at the hotel, there was an awful cabaret," he laughs.
Scandinavia is another part of the world that didn't strike a chord with the composer.
"I'm sorry to all Norwegians, but Norway was boring. One fjord, and you've seen them all." Finland didn't fare much better.
"We were touring Europe in 1993 and arrived in Helsinki. I've never seen so many people drunk in one city before," he recalls. "Wherever you went, hordes of people were bumping into you. It must be the lack of sunlight that drives them all to it, or something."
Mark-Anthony Turnage's work is being performed in the biggest festival ever at London's Royal Festival Hall from 3-18 April