The Duke and Duchess of Cambridge have spoken about their struggle to decide what to do at Christmas.

William and Kate told students in Cardiff they were still wrestling with their plans and had not yet settled on where or with whom they would be spending the festive season.

The Cambridges met undergraduates from Cardiff University, Cardiff Metropolitan University and the University of South Wales at a winter wonderland and food market at Cardiff Castle to hear about the mental health challenges they faced during the pandemic.

It was the first stop on the final day of their country-wide tour by royal train.

As they chatted about arrangements for Christmas, William told the students: “It is so difficult. We are still trying to make plans. It’s difficult to know what to do for the best.”

Lily Faulkner, a 21-year-old second year politics and international studies student at Cardiff University, said afterwards: “They were trying like the rest of us to make Christmas plans with their family and still weren’t 100% sure of what they were going to do or where they were going to be.”

William commented that it was “the first jab today”, with the news that British grandmother Margaret Keenan has become the first in the world to receive Pfizer’s Covid-19 vaccine outside a clinical trial, as the NHS began its mass vaccination programme across the UK.

He asked the group: “How have all you guys been? Have you been able to make any Christmas plans?”

Under a relaxation of the coronavirus rules, three households can mix from December 23 to 27, but the bubble must be exclusive over the five-day period, meaning people cannot shift from one group to another.

The Cambridges and their children Prince George, Princess Charlotte and Prince Louis could spend Christmas with the Middleton family in Berkshire, or have them to stay at their home Anmer Hall in Sandringham, Norfolk.

But Carole and Michael Middleton have two other children as well as Kate – Pippa Matthews and James Middleton, meaning one of the three offspring would not be allowed to gather.

William’s father the Prince of Wales and stepmother the Duchess of Cornwall will spend Christmas Day at Highgrove, their Gloucestershire home, but are expected to see the Queen and the Duke of Edinburgh at Windsor at some point over the holidays, with Camilla also visiting her family.

The Queen, 94, and Philip, 99, have already opted to celebrate a quiet December 25 alone at Windsor.

William and Kate, who was dressed in a Welsh dragon red Alexander McQueen winter coat, with tartan scarf and matching tartan skirt, also took part in a Secret Santa gift swap with six student housemates who had bubbled together.

They sat socially distanced on wooden benches as they all tore off the wrapping paper.

Kate sent the group into giggles when it emerged she had given Gwennan Lewis, 20, from Newport, a £13.99 Prosecco Pong game.

It comprises several plastic glasses and balls and involves participants taking turns to throw a ball into their opponent’s glass and take a drink every time someone shoots and scores.

William bought Dewi Morgan, 19, who is in his second year studying sport and exercise science at Cardiff Metropolitan University, a finger table football game.

The duchess was given a traditional Welsh love spoon, while William laughed at his Guinness beer mat flipping game, adding: “I think this says a lot about me.”

He told the group: “I really hope you get to see your families this Christmas.”

Kate asked whether they had had much mental health support, and was told by Mr Morgan: “As a house we have all supported each other. Some students have felt really isolated but have been very lucky.”

He added he had been tempted to buy the duke a box of hairbands in a humorous nod to his thinning hair, but said: “I bottled it. I bottled it. We could only spend a fiver and I thought the game would be a laugh.”

Ms Lewis said of her present from Kate: “I like the Prosecco Pong, it’s fun. Something to do at Christmas.”

The duke and duchess also toasted giant marshmallows on a fire pit.

Kate, who got some of the sticky sweet treats on her gloved hand, said: “I’m going to have that marshmallow on my fingers all day.”

She said she ordered large marshmallows for George, Charlotte and Louis for their bonfire night celebrations because small ones normally slip off onto the fire.

“I ordered them for the children. There was a bit of a sugar rush,” she added.

Welsh entertainer Max Boyce read his moving poem When Just The Tide Went Out.

It went viral earlier in the year and recalls the highs and lows of lockdown and pays tribute to the NHS.

He added lines in honour of the royal visitors: “And I’ll remember nurses who stretchered all the pain, who Kate and William came to thank, on the Queen’s royal train.”

Mr Boyce told William and Kate afterwards: “It is a great honour and privilege to be asked to read you my poem. I wrote this at the height of the pandemic when all Wales was in lockdown.”

Kate replied: “Well done, fantastic. It was lovely.”

William asked: “How long did it take you to write?” He was told two weeks but that Mr Boyce only had since Monday morning to come up with his extra lines in their honour.

“Oh sorry,” the duchess said. “It’s difficult to change something already written.

“Well done, it really captures what the nation was feeling. It was very, very moving.”

They were seen to smile slightly when Mr Boyce read out his lines: “And I prayed last week for Boris, who knocked on Heaven’s door, And I thought of voting Tory, which I’ve never done before.”