King Charles jokes he has ‘sausage fingers’ with Prince William at the rehearsal for his Coronation ceremony

It's a rare public moment of affection between father and son and ends in a fit of laughter.

As he practices presenting King Charles with his 'Stole Royal', an embroidered band of cloth symbolizing the sacred nature of royalty, ahead of May's coronation, Prince William jokes about how tricky the catch is and groans: 'The day it doesn't go in, eh?'

“No,” says the king, giggling; '[But] you don't have sausage fingers like mine!'

The funny interaction is one of the highlights of a new documentary about Charles' first year as monarch, which will be shown on BBC One on Boxing Day.

Featuring never-before-seen behind-the-scenes footage and exclusive interviews with key officials, family and senior royals, it captures the galloping pace of the past twelve months, as well as moments of lightness.

During rehearsals for May's coronation, during which he swore allegiance to his father, William is shown joking about which of his cheeks to kiss by tickling his father's face and saying, “Your left cheek is better!”

Charles' fingers have attracted attention before, with some jokingly comparing them to sausages

The King is also seen kissing his daughter-in-law, the Princess of Wales, and three grandchildren, Prince George, Princess Charlotte and Prince Louis, warmly as they attend rehearsals.

In the ballroom of Buckingham Palace, which has been converted into a full-size replica of Westminster Abbey, complete with mannequins, you can also see Charles urging the Archbishop of Canterbury, Justin Welby, to be a little bolder with his crown.

The Archbishop says: 'I say a prayer with the crown above. And then slowly lower it, tilting forward.”

The king intervenes: 'You must continue. It has to come here first.”

The Archbishop jokingly protests, “I don't want to break your neck, sir. It could ruin the service.”

Charles replies, “No, you don't. Otherwise I promise you: it's so big, it must fit right and there's nothing I can do about it.'

Asked by Graham Usher, the Bishop of Norwich, to kneel for her anointing, the Queen cheerfully says, “Yes, right!”

Camilla's good friend, Lady Landsdowne, one of her two ladies present at the coronation, comments of her: 'She knows when to be serious.

“And she knows when to wink at a bishop, but [also] when not, which I think is a rather endearing quality.”

King Charles during his coronation rehearsal in Westminster Abbey

The king also comments on the limited guest list, as he sympathizes with the Bishop of Durham, who says he will have to leave his wife at 'the Novotel right opposite Lambeth Palace' to watch the event on television.

“It's so frustrating that we can't just have other halves here,” says Charles.

The documentary, written and co-produced for Oxford Films by The Mail's royal expert Robert Hardman, follows the monarchs as they see their three crowns reworked to suit them and their robes embroidered, sometimes leaving the king looking teary and looks emotional.

After the coronation itself, Lady Lansdowne reveals that there was 'quite a funny moment' in Westminster Abbey when Camilla appeared to back away from the crown.

“But I think that was only because she was afraid the archbishop would step on her dress, so she just backed away,” she says.

The Queen's sister Annabel Elliot, her other Lady in Attendance, added: 'She was clearly incredibly nervous. She doesn't show it often, but I know her well enough.

'I think that he [the King] was very proud of her. And I think there was a feeling of, 'I can't believe it. We did it.'

You can even see Camilla puffing out her cheeks in relief as they arrive back at Buckingham Palace after the formal elements of the day.

Princess Anne explains: 'Just ask an actor who comes off stage after a performance that he or she has really put a lot into, it's a kind of relief.'

Charles greets his sister lovingly and kisses her hand in the same image fragment. “Hello old bean,” he says, smiling broadly.

In another amusing moment, filmed at Balmoral last summer, the king can be seen leafing through his red box of paperwork with his private secretary Sir Clive Alderton.

Asked to sign a message to the King of Sweden on the occasion of his Golden Jubilee, Charles says: 'Oh gracious, is this in Swedish? I hope that's true, right, the Swede? You never know when someone has told you something scary!'

Sir Clive later tells the interviewer: 'The King is an incredibly hard worker. I think that's one of the things that pretty much everyone knows about him. He works very late at night, often well past midnight.”

In their first year alone, Charles and Camilla completed 571 assignments and three state visits, met more than 2,000 people and conferred 1,000 awards.

• Charles III: The Coronation Year will be shown on BBC One on Tuesday 26 December at 6.50pm.