Crowds in the city gave them a warm welcome on Thursday as they also viewed floral tributes in St Ann’s Square and a book of condolence at the Central Library.
The couple travelled to Manchester a day after they paid their respects with the rest of the royal family at Westminster Hall, where the Queen is lying in state.
Members of the public have flocked to the cathedral since the monarch’s death to sign a book of condolence and light a candle.
They were also shown photographs of the Queen’s last visit to the cathedral, to mark the 600th anniversary celebration of the collegiate church in July 2021.
Earlier, city council leader Bev Craig showed Edward and Sophie similar books of condolences opened at the library’s reading room, where they also looked at a number of cards written by local children.
The royal couple then moved on to St Ann’s Square which, in May 2017, was filled with bouquets of flowers and heartfelt messages and tributes in the wake of the Manchester Arena bombing in which 22 people were killed.
Floral tributes and messages of condolence have been left in the square again in large numbers in memory of the Queen.
Prince Edward lay a floral tribute as he inspected the bouquets surrounding the statue of free trade campaigner Richard Cobden.
The Queen’s youngest son shook hands with people lining the square as they offered their condolences, while Sophie embraced one young well-wisher.
Council employee Juliet Felstead, 27, who is leading a team of volunteers overlooking the site, spoke to Edward.
She said: "He was just really grateful for all of the volunteers who have been out over the week to oversee the tributes."
They were both touched by all the messages and the kindness that has been shown.
"We have seen a steady stream of people, with many sharing their memories of the Queen, including some ex-service personnel. It’s meant a lot to people."
The cards and messages will be saved and later archived at Manchester Art Gallery, as the Arena bombing tributes were.
Outside the cathedral one woman said to the earl: "We really appreciate you coming… we are just so sorry for your loss."
She offered her hand which Prince Edward shook and then told her: “Thank you."
The royal couple continued to greet members of the public and thank them for their support before the crowd clapped and cheered as they departed the city.
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