But after being asked by the British Foreign Office to present an Anglo-American enquiry with a plan to stop the bleeding, he failed to prepare.
Mr Nagel explained: "I had to appear in front of this commission, and I had no idea what I was going to say.
"But while talking to them, it came to me. I said: 'If you want to save this business [because the danger was that America would ban the importation of diamonds, which would have been the end of the business] the only way is to establish a worldwide system whereby, if I export to another diamond firm, then I have to give a guarantee that my goods aren't blood diamonds'.
"And the bigger the firm, the higher the fine if they were caught, and they accepted that. And that's called the chain of warranties."
His idea, now known as the Kimberley Process, was subsequently adopted by the United Nations in 2003, and earlier this year earned him a Lifetime Achievement Award from the World Federation of Diamond Bourses.
When asked if he was proud of this industry-saving success, he said simply: "Yes. That's why I'm telling you."
With a strong Romanian accent that he maintained during his time in Palestine and since moving to London nearly seven decades ago, he spoke about witnessing the build-up to the Second World War.
"From my house in Chernowitz I saw all these refugees running away from Poland, in their carriages, all just to get away.
"An hour after the announcement that Romania would be neutral in the war, my father, being an entrepreneur and having common sense, said: 'Tonight, we're going to Palestine'. I didn't believe it."
Mr Nagel recalled getting a small piece of revenge on the country where growing up he had been subjected to antisemitism.
In the early 1990s, with Romania in turmoil following the collapse of the Soviet Union, the Romanian ambassador in Britain, who was a friend of Mr Nagel, approached him and asked if he would purchase two ceremonial swords for his homeland.
After doing so for £60,000 at London auction house Christie's, he was flown to Romania for a congratulatory dinner with the government.
"Then the speeches started," he recalled. "The president said that what I did for Romania in returning the swords, nobody would have done, only someone who was in love with his place of birth. He forgot or didn't know what happened to me in Romania."
Mr Nagel immediately challenged this notion. "I got up, and said 'I'll tell you, Mr President, what happened to me' .
"I told him that, when I started in Chernowitz I went to the best private school. There was a quota for Jews, and one day the music teacher called me up in front of the class of six Jews and 54 non-Jews and asked me to sing a song.
"As soon as he heard my voice, he pulled my ear and said 'You dirty Jew, you call that singing?'. I started to cry. The other Jews cried, and the goyim were absolutely full of laughter.
"I will never forget the politicians' faces. Blank, and very embarrassed. Some people told me afterwards that it was very dangerous for me to make such statements, but I wanted to tell them what I thought.
"The president said I only did it because I loved Romania, my birthplace. Romania, which called me a dirty Jew."
When Mr Nagel first arrived in London from Palestine, he recalled: "It was cold and the food was terrible. It was miserable. I was coming back from a date in Wembley and I couldn't see my finger in front of my face for all the fog."
Then a 24-year-old entrepreneur, he realised he needed a university education to get ahead, and looked for the most reputable institution he could find.
Although he called his entry into Cambridge "a fluke", it was borne out of his determination to never take no for an answer.
"I wrote a letter to the dean of the faculty of international law, saying I'd like to meet him, though I didn't say what for. He invited me, thinking I was some lecturer from India or something.
"When I arrived, his wife said: 'Who is that young boychick arriving there?' But I was already there. They could do nothing about it."
The dean made an exception and Mr Nagel was soon enrolled on a course.
It was at Cambridge that he first became involved with the diamond trade, going on to become one of only a handful of diamond brokers for De Beers - the most powerful firm in the industry. He then started his own business, all before he was 30.
Over the years, his success ensured that he moved in increasingly prestigious circles, striking up friendships with Margaret Thatcher and Princess Diana among others - all of whom are celebrated in pictures which adorn his grand office in central London.
One of the photos is of The Queen, beaming. Mr Nagel also smiled as he recalled their meeting.
"The Israeli president, Ezer Weizman, was here in London, and I was invited to be one of the guests at a dinner at Spencer House. I didn't like it, so before the dessert I went downstairs, which I didn't realise was against protocol."
While he was waiting for the meal to end, the guests of honour came downstairs to see the rest of the house.
"Weizmann had studied with me in London and we had become friends. He left the Queen, the Duke of Edinburgh and his wife and came up to me. He said how nice it was to see me and asked what I was doing now.
"Then we all went to another room, and there were 100 people on the other side of the door, waiting to be introduced to the Queen. Weizman went to join the crowd and the Duke and Mrs Weizman did the same, so the Queen was left alone.
"That was my moment. I approached her, and she was very happy that I rescued her, because no-one was there, and she should always have somebody.
"She gave me her hand and I said to her: 'Madam, you're much better looking in real life than in photographs'.
"That's when she fingered her jewels, as you can see in the photo, and smiled, which you don't often see.
"She was so flattered that she kept on talking to me for 15 minutes about Israel, Weizman and the Arabs, until an Israeli official came up to her trembling, saying: 'Your majesty, there are 100 people waiting to meet you'.
"She answered: 'I know,' and he said: 'Do you want to go?' She replied: 'No, I'm not in a hurry'. That was a very fine moment for me."
The father-of-four, who has two of his children working with him at the company, said that, as well as enabling him to meet a host of international leaders, being a diamond broker had meant he could "live in comfort all my life".
He added: "I don't really regret anything, but I may have made mistakes. I didn't kill anyone."
Although he repeatedly suggested that his accomplishments were down to good luck, he later revealed a more important reason for his success.
"You must have the answers at the right time, and the presence to carry it out."
Throughout his life, Mr Nagel has had both.
