But as with many legendary tales, it turns out the facts are not quite as told.
More than 20 years after the infamous incident, Jeffrey has finally revealed that the delicate 100-year-old cup was not kicked down Princes Street, but was dropped after being used as makeshift rugby ball.
Rugby legend Jeffrey was capped 40 times for Scotland and starred in the side that won the 1990 Grand Slam.
Nicknamed the White Shark because of his distinctive hair, he is infamous for the post-match prank in 1988 when, after Scotland lost 9-6 to England at Murrayfield, he took the revered trophy out on the town alongside England player Richards.
Until now, both men have remained relatively tight-lipped about what happened, denying the kicking story, but claiming the cup had been dropped.
But in a radio interview to be broadcast later this week, Jeffery has finally come clean.
"It was stupid high jinks gone wrong," he said. "But it was certainly not kicked around like a football. It was thrown – but it was dropped."
The player was given a five-month ban by the Scottish Rugby Union after the famous trophy was discovered in the morning, bashed and misshapen.
The incident occurred after the 1988 England-Scotland bout at Murrayfield. Jeffrey has now admitted that on the bus back to the hotel, where the two teams were staying and due to have dinner together, the Scotland team were drinking a mix of Drambuie and whisky.
"It's a chapter of my life that I am not terribly proud about. There were four Scots in bed before the end of the dinner – I so wish I had been," he said.
"Dean Richards and I had the cup and we spotted Brian Moore in the corner and said, 'Come on, let's go and pour the whisky over him'. So we emptied the contents of the cup over his head and ran. It was absolutely schoolchild behaviour.
"The first door we saw was open, so out we went and we saw a taxi. We jumped in and found ourselves in the middle of Edinburgh with the Calcutta Cup. We visited two or three hostelries and the cup got damaged during that time. I remember looking at it – and I must have sobered up. I thought, 'Good Lord, this is a bit of a mess.'
"We took it back to the hotel, handed it in to reception and bolted. I went to bed and waited for the knock on the door, which came at breakfast time the next morning. I got up and said, 'Yeah, I took it out with some player' – I didn't name Dean – 'and I brought it back and I'll take responsibility for it'."
Though the shame has finally passed, Jeffrey is still angry about the inequality of the punishments received by him and Richards, who was given just a one-week ban by England.
"I didn't object to the sentence I got," he said. "What I did object to was the fact that there were two of us involved, two of us took the rap and one gets five months and one gets one week, which was totally out of kilter. It was very disproportionate."
The 1878 cup was presented to the Rugby Football Union by the Calcutta (Rugby) Football Club after they decided the climate in India was too hot for rugby. There were 60 silver rupees left in the club funds when they decided to disband, and they were melted to make the cup.
Jeffrey, who is also famous for his strong feeling against England, said in the interview that he scored against Scotland when playing for English Universities as a student in Newcastle.
Stuff of Legends, BBC Radio Scotland, is broadcast on Thursday 1 July at 11:30am.