William said the sight had left them surprised. "In Scotland, how many rainbows turned up? You hardly ever see rainbows up there, but there were five."
Kate replied, smiling, "Her Majesty was looking down on us."
During the meeting, which marked their first in person engagement since the Queen's funeral, William said he "choked up" when he saw tributes like the Paddington Bear toys left among piles of flowers for the queen, but found comfort in the huge outpouring of public support.
The skies seemed to bid a final farewell to the monarch - Britain's longest-reigning. Rainbows also appeared at Windsor Castle, where she spent most of her time after the death of her husband Prince Philip in April last year.
Rainbows were also seen above the miles-long queue of thousands of mourners lining up to see the Queen lying in state.
Rainbows were also spotted above Elizabeth Tower, which holds the bell of Big Ben, and outside Buckingham Palace and Windsor Castle on the day she died.
Royal duties recommenced yesterday for Prince William, as he made his first speech since his grandmother died with a pre-recorded address to the New York Earthshot Prize summit. He was due to attend in person but cancelled his trip after the Queen's death.
According to Buckingham Palace, the royals will now undertake a small number of engagements to thank those involved in organising the Queen's funeral and associated ceremonial events, and to recognise service to the King and country of those on deployment overseas.
