King Charles, William greet well-wishers in queen's queue

King Charles III meets members of the public in the queue along the South Bank, near to Lambeth Bridge, London, as they wait to view Queen Elizabeth II lying in state ahead of her funeral on Monday. Aaron Chown/Pool via REUTERS

* Queen Elizabeth's grandchildren to hold vigil * Line to see queen's coffin stretches to 16.5 hours * World leaders start arriving in London for funeral King Charles and his son William shook hands and greeted well-wishers who had queued for hours in central London on Saturday to file past the coffin of Queen Elizabeth, asking people how long they had been there and whether they were warm enough. To cheers of "hip, hip, hurrah" and shouts of "God save the King", Charles and William spoke to mourners near Lambeth Bridge, as they neared the end of the mammoth line to see the lying-in-state in the historic Westminster Hall. On Friday night, Charles had joined his three siblings -- Princess Anne and Princes Andrew and Edward -- in a silent vigil at the coffin while their eight children, including William and Harry, will form their own ceremonial guard later on Saturday. "She wouldn't believe all this, she really wouldn't," William was heard telling one man of the late monarch who died on Sept. 8 at the age of 96. "It's amazing." One woman told Charles it had been "worth the wait" and others wished him well when he asked how long they had been standing there. People continued to flock to central London, adding to the hundreds of thousands who have filed past the coffin in a solemn stream to honour Britain's longest-reigning monarch - a testimony to the affection in which she was held. Ahead of the state funeral on Monday, world leaders also starting arriving in the British capital. Canadian Prime Minister Justin Trudeau and Australian Prime Minister Anthony Albanese were among the dignitaries to pay their respects on Saturday while New Zealand Prime Minister Jacinda Ardern was seen curtsying to the coffin on Friday. US President Joe Biden was expected to go on Sunday to see Elizabeth lying in state in an oak coffin on a purple-clad catafalque, draped in the Royal Standard and with the bejewelled Imperial State Crown on top. London's police force has described the funeral as the biggest security operation it has ever undertaken as prime ministers, presidents and royals come together, and the king visited police headquarters to thank emergency services workers involved in the planning on Saturday. Underscoring the risks, police said one man had been detained and arrested after a witness told Sky News he "ran up to the queen's coffin". Footage showed a man being pinned to the ground by police officers and taken away. Charles was also due to greet leaders of the 14 countries where he is head of state such as Canada, Australia, and Jamaica after meeting the governors-general - the people who represent the monarch in overseas realms - at Buckingham Palace. By 2 p.m. (1300 GMT), Britain's culture ministry said the waiting time to reach Westminster Hall was up to 16.5 hours. Inside the silent hall, some mourners wept, many were tearful while current soldiers and veterans saluted their former commander-in-chief. Others fell to their knees. At one point the government had warned it would pause entry to the queue if demand became too high, adding at 1 a.m. (0000 GMT): "Please do not travel." New friendships, acts of kindness and the struggles of standing in line for hours, sometimes overnight, have come to define what has become known as just "the queue". Film-maker Matthew West described how a military man was offered the chance to get to the front but declined. "That was the highlight. The lowlight was when we stood still for two hours and I lost the will to live." The death of the queen at her summer estate in the Scottish highlands has sparked an outpouring of emotion across the country and 10 days of choreographed events. Having laid at rest in the Scottish capital the coffin was flown south to London, where tens of thousands of people crowded onto a normally busy road in driving rain to observe the flag-draped casket being driven to Buckingham Palace. FUNERAL PLANS The queen's children have described being overwhelmed by the reaction to their mother's death. The state funeral, to be attended by nearly 100 presidents and heads of government is likely to be one of the biggest ceremonial events ever held in Britain. Soldiers took part in early morning rehearsals in Windsor, where the queen's coffin will be taken after the funeral at Westminster Abbey. Marching bands playing music and Grenadier Guards, who wear a tall bearskin hat on ceremonial duties, were seen marching down the High Street in preparation. Later on Saturday, the focus will switch to the younger royals and their vigil. William and his brother Harry, who have grown apart in recent years after Harry moved to the United States, will both stand guard at the coffin in military uniform. Harry served two tours of duty with the British Army in Afghanistan but so far has appeared in processions in morning suits after he lost his honorary military titles when he stepped back from public royal duties. The two brothers will be joined by their cousins - Peter Phillips and Zara Tindall, the children of Princess Anne, Princesses Beatrice and Eugenie, the children of Prince Andrew, and Louise and James, the children of Prince Edward.