Prince William and Prince Harry don uniform in vigil by queen's coffin

King Charles' sons joined by their six cousins on Saturday evening to stand around their grandmother's casket

Prince William, right, and Prince Harry attend the vigil by Queen Elizabeth's grandchildren around the monarch's coffin in the Westminster Hall, in London. AP

Heir to the British throne Prince William and his brother Prince Harry stood vigil at either end of the coffin of their grandmother Queen Elizabeth on Saturday, heads bowed, as a line of mourners who had braved a queue of up to 24 hours streamed past the late monarch's lying in state.

The two sons of King Charles, attired in military uniforms, stood in silence for 15 minutes in the vast Westminster Hall where the coffin has been placed since Wednesday, draped in the Royal Standard and with the bejewelled imperial state crown on top.

The princes were joined by their six cousins, including Princess Beatrice and Princess Eugenie, who earlier paid tribute to Britain's longest-reigning sovereign, after she died on September 8 at her summer estate, Balmoral, in Scotland, aged 96.

"You were our matriarch, our guide, our loving hand on our backs leading us through this world," said the sisters, daughters of Prince Andrew. "You taught us so much and we will cherish those lessons and memories forever. For now dear grannie, all we want to say is thank you."

Hundreds of thousands of people lined up for long hours in a queue stretching along the Thames, waiting to file past the coffin and honour the queen — a testimony to the affection in which the monarch who ascended to the throne in 1952 was held.

The other cousins at Saturday's vigil were Peter Phillips and Zara Tindall, the children of Princess Anne, and Louise and James, the children of Prince Edward.

Earlier on Saturday, King Charles and Prince William shook hands and greeted mourners in the queue, 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", the royals spoke to mourners near Lambeth Bridge, as they neared the end of the enormous line to see the lying in state in the Westminster Hall.

On Friday night, King Charles joined his three siblings — Princess Anne, Prince Andrew and Prince Edward — in a silent vigil at the coffin.

"She wouldn't believe all this, she really wouldn't," Prince William was heard telling one man of the late queen, who came to the throne in 1952. “It's amazing."

One woman told the king it had been "worth the wait" and others wished him well and cheered as he moved down the line.

Before the state funeral at Westminster Abbey on Monday, world leaders started arriving in the British capital.

Prime Ministers Justin Trudeau of Canada and Anthony Albanese of Australia were among the dignitaries to pay their respects on Saturday while their New Zealand counterpart Jacinda Ardern was seen curtsying to the coffin on Friday.

Mr Trudeau signed a book of condolence at Lancaster House on Saturday for the queen.

Prime Minister Justin Trudeau of Canada signs a book of condolence at Lancaster House, in London. AP

Mr Trudeau, who met the monarch as a young boy when his father Pierre Trudeau was prime minister, signed the book along with his wife Sophie.

US President Joe Biden was expected to attend the lying in state on Sunday.