Queen Elizabeth II's eight grandchildren mounted a vigil around her coffin on Saturday, hours after King Charles III and his heir Prince William staged an unscheduled London walkabout to thank those queueing overnight to pay their last respects.

Displaying maturity above his years, the late Queen's youngest grandchild James, Viscount Severn, stood vigil beside his grandmother's coffin along with his sister, Lady Louise Windsor, and cousins.

Prince William and his estranged brother Prince Harry led the 15-minute vigil inside parliament's Westminster Hall, which has hosted tens of thousands of mourners since the late queen began lying in state there on Wednesday.

The grandchildren, aged from 44 to 14, stood silently with their eyes lowered as members of the public filed past.

Harry — who served two tours with the British Army in Afghanistan — wore his military uniform, despite no longer being a working royal, after being given special permission by his father.

The move appeared to be the latest olive branch offered by King Charles towards his youngest son after Harry and his wife Meghan, now living in California, accused the royal family of racism.

An impromptu walkabout by the king and his eldest son William earlier delighted mourners who had queued all night to see Queen Elizabeth's coffin before Monday's grand state funeral.

Cries of "God save the king" came from the riverside crowd as the royals thanked the well-wishers waiting patiently in line before Charles went on to meet some of the many world leaders arriving for Monday's lavish send-off.

"I'm so happy. He was so calm, and friendly and he was so gentle," said Geraldine Potts-Ahmad, a secretary in her late 50s, as she struggled to contain her emotions after shaking hands with King Charles.

"He is going to make the best king. That gentleness and that tenderness — I saw the queen in that."

Queen Elizabeth's death on September 8 aged 96, after a record-breaking 70 years on the throne, has sparked an outpouring of emotion.

Tens of thousands of people are braving waits that have stretched to more than 25 hours to view her coffin.

Volunteers handed out blue blankets to guard against the night-time chill.

Fainting

The somber occasion was briefly disrupted late on Friday when a man burst out of the line and approached the coffin, which sits topped with the Imperial State Crown.

But otherwise, the mood remained reverential on Saturday as people walked slowly past the catafalque, bowing their heads, clasping their hands in prayer, or saluting in the case of some veterans wearing medals.

Some 435 people in the queue have needed medical treatment, often for head injuries after fainting, the London Ambulance Service said.

But Alison Whitham, an ex-nurse from Ashby in the English Midlands, said her 14-hour wait was well worth it after paying her final respects.

"It was very moving, very dignified, blissfully quiet," the 54-year-old said.

"The fact that you could just concentrate, with nobody holding phones up, was so lovely."

Police are mounting Britain's biggest-ever security operation for Monday's funeral, with hundreds of dignitaries including US President Joe Biden set to jet in and mourners already setting up camp in front of Westminster Hall and Buckingham Palace for the final goodbye.

"I went to princess Diana's funeral when I was a teenager, I was right outside the abbey, and the atmosphere was incredible," said Magdalena Staples, 38, who was camping outside Westminster Hall with her two children, aged nine and 10.

"I wanted my children… to have the same experience. We're camping for three nights, we've got hot clothes, snacks, a mattress, and toilets nearby," she added.

Less than two weeks since she was appointed by the late queen, British Prime Minister Liz Truss was on Saturday beginning a packed series of meetings with world leaders including New Zealand counterpart Jacinda Ardern and Australia's pro-republic PM Anthony Albanese.

Ardern, Albanese, and Canadian Prime Minister Justin Trudeau were among leaders who paid their respects at Westminster Hall.

They later held one-on-one talks with their new king as he received leaders of the Commonwealth realms — the 14 countries over which he now reigns in addition to the United Kingdom — at Buckingham Palace.

From Australia and Canada to Jamaica and Papua New Guinea, they have formally proclaimed him their new sovereign.

But republican movements are gaining ground in many of the countries, and efforts to keep them all in the royal fold will likely be a feature of his reign.

Biden was expected to visit Westminster Hall on Sunday.

'Tide of emotion'

After visiting Wales on Friday, Charles joined a 15-minute vigil with his siblings — Princess Anne, Prince Andrew, and Prince Edward — around their mother's casket.

The personal sorrow of the queen's family has been playing out in the glare of intense international attention.

Her granddaughters Princesses Beatrice and Eugenie, who were part of Saturday's vigil, paid a heartfelt tribute to "our dearest Grannie".

"We, like many, thought you'd be here forever," the sisters said. "And we all miss you terribly.

"You were our matriarch, our guide, our loving hand on our backs leading us through this world. For now dear Grannie, all we want to say is thank you," they added.

The public have until 6:30 am (0530 GMT) on Monday to view the coffin before the queen is honored with Britain's first state funeral in nearly six decades.

The spectacular ceremony at Westminster Abbey — expected to be watched by billions around the globe — will see 142 sailors pulling the gun carriage bearing her lead-lined coffin.

It will be attended by more than 2,000 guests, but leaders from countries at loggerheads with the UK such as Russia, Belarus, and Afghanistan have not been invited.

China's vice president Wang Qishan will attend, Beijing's foreign ministry confirmed after a diplomatic spat saw Chinese officials barred from visiting the coffin inside parliament.