“Within a couple of minutes they were asleep, and died within 10 minutes,” Caractacus Downes, the couple’s 41-year-old son, said in the interview after his return to Britain. “They wanted to be next to each other when they died.” He added, “It is a very civilized way to end your life, and I don’t understand why the legal position in this country doesn’t allow it.”

Sir Edward, who was described in a statement issued earlier on Tuesday by Mr. Downes and his sister, Boudicca, 39, as “almost blind and increasingly deaf,” was principal conductor of the BBC Philharmonic Orchestra from 1980 to 1991. He was also a conductor of the Royal Opera House at Covent Garden in London, where he led 950 performances over more than 50 years.

Lady Downes, who British newspapers said was in the final stages of terminal cancer, was a former ballet dancer, choreographer and television producer who devoted her later years to working as her husband’s assistant.

“After 54 happy years together, they decided to end their own lives rather than continue to struggle with serious health problems,” the Downes children said in their statement.

British families who have used the Zurich clinic in the past have said that Dignitas charges about $6,570 for each assisted suicide.

Scotland Yard said in a statement on Tuesday that it had been informed on Monday “that a man and a woman” from London had died in Switzerland, and that it was “looking into the circumstances.” The information that prompted the police inquiry appeared to have been given voluntarily by the Downes family, which, Caractacus Downes said, “didn’t want to be untruthful about what had happened.”

“Even if they arrest us and send us to prison, it would have made no difference because it is what our parents wanted,” he said.

Attempting suicide has not been a criminal offense in Britain since 1961, but assisting others to kill themselves is. But since the Zurich clinic run by Dignitas was established in 1998 under Swiss laws that allow clinics to provide lethal drugs, British authorities have effectively turned a blind eye to Britons who go there to die.

None of the family members and friends who have accompanied the 117 people living in Britain who have traveled to the Zurich clinic for help in ending their lives have been charged with an offense. Legal experts said it was unlikely that that would change in the Downes case.

But British news reports about the Downeses’ suicides noted one factor that appeared to set the case apart from others involving the Dignitas clinic: Sir Edward appeared not to have been terminally ill. There have been at least three other cases similar to the Downeses’, in which a spouse who was not terminally ill chose to die with the other.

Sir Edward was known for his support for British composers and his passion for Prokofiev and Verdi. After studying at the Royal College of Music in London, he joined the Royal Opera House in 1952. His first assignment was prompting the soprano Maria Callas. He traveled widely as a conductor and became music director of the Australian Opera in the 1970s.

Friends of Sir Edward said that his decision to die with his wife did not surprise them. “Ted was completely rational,” said Richard Wigley, the general manager of the BBC Philharmonic. “So I can well imagine him, being so rational, saying, ‘It’s been great, so let’s end our lives together.’ ”

Jonathan Groves, Sir Edward’s manager, called their decision “typically brave and courageous.”

But even among those who support decriminalizing assisted suicide, Sir Edward’s death raised troubling questions. Sarah Wootton, chief executive of Dignity in Dying, said in a BBC interview that the growing numbers of Britons going abroad to die, and the manner of their deaths, made it more urgent to amend Britain’s laws.

There are “no safeguards, no brakes on the process at all,” she said. The British Medical Association voted this month against legalizing assisted suicide, or lifting the threat of prosecution from “friends and relatives who accompany loved ones to die abroad.” Last week, the House of Lords defeated a bill that would have allowed people, subject to safeguards, to travel abroad to help people choosing to die.