There, Thompson said he received eight phone calls from the kidnappers over eight hours. Each call lasted around 60 seconds, but the police needed at least 90 seconds to trace the call.
"When the last call came at 1.30 a.m. I managed to keep him talking for one minute and 35 seconds," Thompson said. "I thought, 'That's it, we've got him,' but the police told me 'Sorry Mr. Thompson, the man who does the tracing goes off duty at midnight.'
"That was the best chance we had of catching them and it was gone."
Shergar was owned by a syndicate of 34 people, each with a share worth £250,000 ($394,000). The syndicate refused to pay the ransom, fearing it would encourage other kidnappings.
"The following Monday we received a call saying the horse had had an accident and was dead. That was the last time we heard from them," Thompson said.
Thompson believes the IRA was responsible, pointing to evidence in former member Sean O'Callaghan's 1999 autobiography "The Informer."
"Every time I took a call from the kidnapper I used a different code word -- the name of a famous race horse -- so I would know it was the same guy calling back," Thompson said.
"But there was always one name I kept to myself, I never told anyone else, and when I read O'Callaghan's book it was there. That really shook me to the core."
Jockey Walter Swinburn, who as a 19-year-old rode Shergar to that historic Epsom Derby win, said the kidnapping had a profound effect on tightening racing industry security.
"Shergar's stable was very impressive but anybody could have walked into it," he said. "Today it's more like a padded cell, they can't afford for the horse to get injured, with CCTV and a large number of grooms."
The thoroughbred has since been immortalized in Ascot's annual Shergar Cup and the 1999 film "Shergar" starring Mickey Rourke.
Swinburn regrets that Shergar's achievements on the track will always be overshadowed by his dramatic abduction. But the image of him pounding over the hill at Epsom, his seemingly tiny competitors trailing behind, lives on.