The king’s authorised biography made no mention of the incident. But light has been shed on it by Paul Preston, a professor at the London School of Economics, whose biography laying bare the king’s private life has reached No 2 in the Spanish bestseller lists.

Preston’s book, entitled Juan Carlos, The People’s King, has caused a furore by suggesting the future monarch may have pulled the trigger. It says he admitted to a friend he had been holding the gun at the time.

The professor has given more than 60 interviews to the Spanish media and has been bombarded with hate mail and death threats. A source close to Juan Carlos, 65, has denounced the book as “nasty rubbish”, but the palace has refused to be drawn.

“It’s a highly explosive subject that is still taboo,” said Preston, who has written extensively on the Spanish civil war. “But the fact is the old official statement that claimed a pistol just went off, as if by itself, is pretty inadequate. The king was not a child when it happened but an 18-year-old cadet at a military academy who knew how to handle guns.”

The shooting occurred at Estoril, Portugal, where the royal family was in exile. When Juan Carlos reached 10, his father had been coerced into handing him to General Franco, the dictator. Franco wanted to groom the blond, blue-eyed prince as his successor.

However, on March 29, 1956 Juan Carlos travelled to Portugal to be with his parents. He and his younger brother had returned from mass and were alone in an upstairs room when a single shot rang out. Alfonso was hit in the forehead at close range and died within minutes.

A terse official statement, approved by Franco, said a gun “accidentally went off”, but gave no more details. After the funeral just two days later, Don Juan immediately sent his surviving son back to his military academy in Spain and threw the pistol into a lake.

It is not known where the gun came from, and Juan Carlos has never publicly discussed what he was doing with his brother at the time the shot was fired. There has been speculation that he played a prank, believing that the weapon was not loaded.

Bernardo Arnoso, one of the king’s friends interviewed for the book, claims Juan Carlos told him the gun had been in his hands. “It was the king who had his finger on the trigger,” said Preston. “While most people will accept it was simply an accident, we could of course speculate for hours on his unconscious state of mind.”

Antonio Eraso, another of Juan Carlos’s childhood confidants, told the author that Don Juan may initially have been suspicious. “According to Eraso, the king was taken by his father and made to swear that he didn’t shoot his brother on purpose,” said Preston.

“The king’s relationship with his father was already strained and after that they often avoided contact with each other. I believe that to have experienced such a tragic incident, with all the feelings of guilt that must have arisen afterwards even when we accept it was an accident, must have shaped certain aspects of the king’s character, and that is why I explored it.”

The book, which runs to more than 650 pages, also contains allegations about the king’s love life.

His first love is said to have been Maria Gabriella of Savoy, daughter of King Umberto, the exiled Italian monarch. According to Preston, their liaison was brought to an abrupt end when she was deemed unsuitable by Franco. “In one sense Franco became his surrogate father and took control of almost every aspect of his life, from what he read to who would be his future spouse,” said Preston.

Juan Carlos, blessed with film-star looks, swiftly moved on, supposedly falling in love with Olghina di Robilant, a beautiful but penniless aristocrat from Rome. Robilant reveals in letters and a memoir that she had a long-term sexual relationship with the king before Franco again intervened, Preston said.

“This has certainly provided grounds for speculating that her daughter, born during that period, may have been fathered by Juan Carlos.” The king was eventually permitted to marry Princess Sophia, the daughter of King Paul of Greece.

Preston’s book has been praised for its openness by left-wing politicians and condemned as irreverent by conservatives. Francisco Umbral, a leading columnist, wrote: “What can that fat Englishman possibly tell us?” Some academics believe the book has had strong reactions because the foundations of post-Franco society are relatively weak.

“As the father of Spanish democracy the king has played a stabilising role and anything that could undermine him personally is perceived as having a potentially destabilising influence politically,” said Paloma Gay y Blasco, a Spanish social anthropologist at Queen’s University, Belfast.

“The private life of the king is treated as sacrosanct in pretty much the same way as the private lives of British royals were 50 years ago.”

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