“To my dear mama as you begin your last great journey to join my dear late papa, I simply want to say this: thank you,” King Charles said. The king, quoting Shakespeare’s Hamlet, concluded by saying “flights of angels sing thee to thy rest.”

Sitting in the room where his mother had once recorded Christmas messages to the nation, and wearing a black tie with a picture of Queen Elizabeth next to him, King Charles pledged to both respect the traditions of Britain while embracing those from different backgrounds, recognizing that the country had changed dramatically since the time his mother ascended to the throne.

“Our values have remained and must remain constant,” he said. “Whatever may be your background or beliefs, I shall endeavor to serve you with loyalty, respect and love, as I have throughout my life.”

The king paid tribute to his family. He said that his heir, Prince William, would become Prince of Wales, a title that Charles himself held for many years and is traditionally held by the heir to the throne. He also expressed his love for his younger son,

Prince Harry,

and his wife, Meghan, Duchess of Sussex. He also spoke of his devotion to his “darling wife” Camilla, who became Queen Consort.

The speech looked to put to bed some of the criticism that King Charles had faced for using his station as heir to the throne to bring about societal change on a range of topics including climate change and farming. He said he would no longer be able to give “so much time and energies” to the issues “for which I care so deeply.”

Earlier, the new king arrived at Buckingham Palace and began the work of trying to win over a public in mourning over the death of his popular mother and those more skeptical about his ability to fill her place in the nation’s heart.

Dressed in black, the former Prince of Wales unexpectedly walked up and down in front of the palace to greet thousands of visitors who had turned up to pay tribute to the late queen and their new monarch, shaking hands and exchanging words amid shouts of “God save the king.”

Visitors offered words of condolence to the king about his mother’s death. One visitor handed the king a red rose.

The king and the Queen Consort then walked by the hundreds of floral tributes that lined the gates of the palace before entering inside to applause.

Thousands of Britons and tourists crowded around the palace, some bearing flowers and others waving flags. Visitors who couldn’t reach the gates to place flowers handed them to those ahead of them. Others placed bouquets, crosses, stuffed animals—and even a jar of Robertson’s marmalade, a nod to a recent video the queen made with Paddington Bear—at the base of nearby trees. Many attached handwritten notes, thanking the queen for her dedication and service. Flowers were tied to the railings of Buckingham Palace.

“Even though this was expected in a way, it’s sad, it’s very sad,” said Coralie Perry, 48, who came to Buckingham Palace late Thursday to see the official announcement of the queen’s death posted on the palace gates, what she described as a “massive moment” in the country’s history.

“She was a constant in everyone’s lives, and especially through Covid, she was that one thing that didn’t change,” she said.

Britons mourned and began trying to get accustomed to the idea of having a king for the first time in seven decades. The country’s last king was Elizabeth’s father, King George VI, who died in 1952.

Gerald Newsom, a 78-year-old London resident who said he remembered when King George VI died, said he expected his new king to be quickly accepted by most Britons. “I think he’ll be good, I think he’ll be right for the time,” he said. “Maybe 20 or 30 years ago, it might have been a different story, but I think he’s matured into it.”

Close to Buckingham Palace, several thousand people gathered at Hyde Park to watch a 96-gun salute—one for each year of the late queen’s life—fired by the King’s Troop Royal Horse Artillery, using field guns from the World War I era. The Sebastopol Bell in Windsor Castle, a bell captured from the Russians during the Crimean War in the 19th century, tolled at midday. Flags on royal residences stood at half-staff.

Prime Minister

Liz Truss

met with the new king at Buckingham Palace.

Members of parliament, who just the day before had been engaged in a heated discussion over natural-gas prices, united to pay tribute to the only monarch most had known in their lives. All were dressed in black.

“Whether having tea with 007 or marmalade with Paddington Bear, she brought the monarchy into our lives,” Ms. Truss told fellow lawmakers, to the shouts of “yea.”

Opposition leader

Keir Starmer

quoted poet Philip Larkin: “In times when nothing stood but worsened or grew strange, there was one constant good. She did not change.” And former Prime Minister

Boris Johnson

showed he still had a way with words by offering what some saw as the most moving tribute of the day.

“I think millions of us are trying to understand why we are feeling this deep and personal and almost familial sense of loss,” he said. “But I think our shock is keener today because we are coming to understand, in her death, the full magnitude of what she did for all of us.”

A period of national mourning is expected to last around 10 days, during which some aspects of life in the U.K. will be paused. A planned strike by postal workers on Friday, stage six of the Tour of Britain cycling race and the second day of a cricket match between England and South Africa were all postponed, as were the weekend soccer games of the Premier League. The remainder of the Proms, a well-known series of British classical-music concerts, has been canceled. People visiting Parliament have been advised to wear dark clothing out of respect.

Images of the late queen graced billboards and train stations across the country, as well as the front page of virtually every newspaper. Even normally raucous tabloids like the Sun were subdued: “We loved you Ma’am,” the Sun’s banner headline read. Inside was a 36-page tribute.

France, a country the late monarch visited more than any other, turned off the lights to the Eiffel Tower, and French President

Emmanuel Macron

said, in English: “To you, she was your queen. To us, she was the queen.”

The king said the royal household would be in mourning until seven days after the queen’s funeral, the date of which hasn’t been confirmed. Flags at royal residences will remain at half-staff until the morning after the funeral.

On Saturday, King Charles will visit Parliament where senior ministers will swear an oath to him. That day, a ceremony will take place at St. James’s Palace in London to formally proclaim King Charles III as monarch, after which ceremonial guns will be fired across the capital.

The late queen will lie in rest in Scotland before her body is expected to be flown back to London in a few days’ time. People will then be allowed to file past her coffin to pay tribute for several days.

The day of the funeral in Westminster Abbey, which is expected to be in 10 or 11 days, will likely be declared a national holiday. The queen will be laid to rest at St. George’s Chapel at Windsor Castle, where her husband, Prince Philip, was buried last year after he died at the age of 99.

Aides to King Charles have said the new monarch envisions a slimmed-down and lower-cost royal family that remains at the center of Britain’s national life. To do that, he must unite his family at a time when the House of Windsor is grappling with strained relationships, including the acrimonious split with his son Prince Harry, who quit royal duties in 2020 and has had a strained relationship with his brother William.

King Charles isn’t universally popular with his subjects. With a 42% approval rating, Charles was the seventh most popular British royal in a recent YouGov poll, below his son Prince William. The queen was the most popular, with 75%.

Palace aides said they expect his popularity to rise as the nation gets used to him in the role as king.

King Charles takes over the monarchy at a difficult time for the U.K., with record inflation and a looming recession. Hours before the Queen died, the government said it would spend over £100 billion subsidizing household and business energy bills, which are surging due to the war in Ukraine.

Unlike his mother, who was in her 20s when she became queen and deferred to more experienced courtiers inherited from her father, Charles has had decades to study for the role. Charles, 73 years old, is the oldest man to ascend to the throne, eclipsing William IV, who took over in 1830 at the age of 64.

Lucy Holroyd, a 50-year-old from Reading, was at a pub Thursday evening when she heard the news of the queen’s passing. Overcome with emotion, she began crying. When she woke up Friday, she said, she felt compelled to head to Buckingham Palace.

“I just needed to feel part of it,” she said. “It felt like losing your mum or something.”

Standing close to the front gates of the palace, she met Risé Kirbo and Beverly Young, both 71, who were on a delayed 70th-birthday trip from the United States and decided to stop by the palace to pay their respects.

“When you suffer a loss you want to be around people who are grieving with you,” said Ms. Kirbo, of California. “I’ve just always had such respect for her. She was so real.”

All three women said they were feeling uncertain about a future under King Charles III.

“I feel a bit disturbed. She’s the face of this country. It’s going to be a transition to look at someone else and put them in that place,” said Ms. Kirbo, adding that she feels skeptical of Charles after his divorce from Princess Diana. “I still kind of carry that.”

Sharon Levy, a 65-year-old resident of North London, teared up as she described her affection for the queen. “She represents every woman’s strength. She never got knocked off, she was always focused, she always held herself together,” she said.

Ms. Levy said she didn’t believe Charles should take the throne. “He represents more grief to us—we were all here for the funeral for [Princess] Diana,” she said. “And I think sometimes you have to be big enough to say, ‘I made a mistake and I shouldn’t take the throne.’ This is the end of something.”

Write to Max Colchester at max.colchester@wsj.com, David Luhnow at david.luhnow@wsj.com and Caitlin McCabe at caitlin.mccabe@wsj.com