The queen, accompanied by her husband, Prince Philip, left in a convoy of limousines soon after Prince Charles departed with his sons, William, 15, and Harry, 13.
The princes were due to visit Diana's coffin at St. James's Palace in London today, the day before the princess's funeral.
Buckingham Palace said the speech will begin at 1 p.m. EDT (6 p.m. local time).
The address and the queen's early departure from Balmoral _ she originally planned to come to London on Saturday by Royal Train _ followed claims that the royal family was not sharing in the public outpouring of grief.
On Thursday, Prince Charles appeared in public with his sons for the first time since Sunday. Charles held Harry's hand as the family, along with the queen and Prince Philip, looked at floral tributes left outside the Crathie church, near Balmoral.
In another last-minute change, Diana's brother, the ninth Earl Spencer, announced today that his sister will be buried on an island on the grounds of the family's stately home, Althorp Park, instead of in the nearby village church.
The island is surrounded by an ornamental lake. The change reflected fears that Great Brington, a hamlet of 200 people where the Church of St. Mary the Virgin is located, would be turned into a sort of shrine, overrun by sightseers.
Earl Spencer, who had said Sunday that there was "blood on the hands" of every editor who bought pictures from free-lance photographers who had hounded Diana, intervened Thursday to bar seven tabloid editors from attending the funeral.
With the funeral approaching, there has been no letup in the public surge of emotion. Early today, police estimated that 12,000 people were waiting to sign condolence books at St. James's Palace.
A group of singers gathered at the Queen Victoria monument opposite Buckingham Palace, singing hymns and songs including "The Lord Is My Shepherd" and "Silent Night," joined by a growing number of bystanders.
In Paris, French police detained three more photographers in their investigation of the crash that killed Diana, 36, her new love, Dodi Fayed, and chauffeur Henri Paul. Earlier, seven photographers and a motorcyclist were detained.
The paparazzi could be charged with manslaughter and other crimes. All of those detained have denied claims that the high-speed pursuit of Diana's car caused the wreck that took her life.
Meanwhile, a man claiming to be one of the photographers at the scene of the crash acknowledged in comments published today by the French daily Liberation that he and some colleagues took photos and left without trying to help the victims.
"OK, we took photos without thinking," the man, who was not identified, was quoted as saying. "What was I supposed to do? I'm neither a doctor nor a fireman."
The man, whose interview on the German television program Pro-Sieben was published by Liberation, also joined in claims that the driver was going too fast.
"I have never seen anyone take off like that," he said. "He was driving like a gangster."
The driver, Henri Paul, was legally drunk at the time, prosecutors have said.
Police said Thursday that the Mercedes Diana was riding in had at one time been stolen and stripped before it was repaired. It was unclear whether that affected the car's mechanical functioning.
Sources close to the investigation also said authorities are particularly interested in how the car of one photographer came to be parked in front of the crumpled Mercedes. They are looking into the possibility that the car might have cut off Diana's sedan.
Many Britons on Thursday welcomed the queen's decision to address the nation, an event that normally happens only once a year, at Christmas.
"The queen is in a difficult situation," said Lucille Horgan, 35, who traveled to Westminster Abbey on Thursday from her home in Lincoln, in central England, to lay flowers. "She has so many people to please, and yet she must keep up with tradition."
In the four days after Diana's death, the royal family issued only one public statement.
"Your people are suffering _ Speak to us Ma'am," blared the front page of the Daily Mirror, the newspaper that bought the final paparazzi pictures of Princess Diana alive. The Sun's front page demanded: "Where is our queen?"
On Thursday, the queen said she was "hurt" by the newspaper criticism.
To cope with the expected million or more mourners Saturday, a third giant TV screen _ in addition to two already promised for Hyde Park _ will be erected in Regent's Park, where up to 70,000 people will be able to watch coverage of the funeral, Buckingham Palace said.
And for the first time, the queen has ordered that the Union Jack flag replace the monarch's personal flag _ the blue, red and gold Royal Standard _ over Buckingham Palace on Saturday. It will fly half-staff all day _ another first.
British commentators said anger from some over the queen's reticence rose from a generational gap between her and the majority of Britons.
"'All you need is love' was their central doctrine," columnist William Rees-Mogg said of Diana's generation, born in the 1960s and 1970s. By contrast the queen's generation, brought up in World War II's privation and emphasis on discipline, "was taught to control its emotions."
During the ceremony, Elton John will perform a reworked version of his song about Marilyn Monroe, "Candle in the Wind."
Instead of beginning "Goodbye, Norma Jean," the new version starts with:
"Goodbye, England's rose, may you ever grow in our hearts. You were the
grace that placed itself where lives were torn apart ... "