Prince William spoke out as he and Kate talked by video call to Shivali Modha, who has Type 2 Diabetes and was preparing to have her jabs when she spoke to the royals last Tuesday.
Shivali, who has been shielding with her husband Hiren and daughters Shyaama, 11, and Jyoti, 9, since last March, told the royal couple she had been anxious about the vaccine after reading negative posts on social media, but has since been reassured by family members, medics and the charity Diabetes UK.
The Duke told her: "Catherine and I are not medical experts by any means but if it's any consolation, we can wholeheartedly support having vaccinations. It's really, really important.
"We've spoken to a lot of people about it and the uptake has been amazing so far. We've got to keep it going so the younger generations also feel that it's really important for them to have it.
"So it's great that Shivali you're taking the time to work it out and come to the conclusion that 'I need to do this' because social media is awash sometimes with lots of rumours and misinformation so we have to be a bit careful who we believe and where we get our information from.
"Especially for those who are clinically vulnerable as well, it's so important that those vaccinations are done, so good luck."
Shivali replied: "I guess it's just the unknown and I think that's the case for most people."
The couple spoke with Shivali, her husband Hiren and their daughters
Kate told her: "I hope it comes as a huge relief in the end. I know there's maybe the anxiety and the worry leading up to it, but I hope for all of you it will add a bit of normality back to your lives and confidence as well as we go forward into the spring, that would be great."
Thanking the Duke and Duchess for calling, Shivali told them: "It's really nice to have you in our home, I wish I could offer you a cup of tea!"
"Same here!" laughed Kate.
William added: "We quite like the sound of the fancy dress evenings, we might come around for one of those!"
William and Kate also spoke to Fiona and her daughter Ciara
The Duke and Duchess also spoke to Fiona Doyle and her seven-year-old daughter Ciara, who have been shielding at home in East Finchley, north London because of Fiona's severe asthma.
Fiona said of having to start shielding last March: "It was difficult because I'm a single parent as well so I kind of have that extra layer of wanting to feel invincible and wanting to feel like there’s nothing that could ever harm me or hurt me or my child.
"So then knowing that there was this virus out there that was incredibly dangerous for me, it was really difficult."
She said the charity Asthma UK had been a "real source of support" in dealing with her situation.
Asked by the Duke how she felt about the vaccination, she replied: "I can't wait!
"I have always been somebody who truly believes in vaccines, and I truly believe in science and medicine. I think that it's the best way to look ahead to have a much brighter future and go back to normality."
William visited a vaccination centre in King's Lynn on Monday
The royal couple also spoke to Ciara about home schooling and Kate asked her: "Are you missing your friends Ciara?"
"Yeah a lot," she replied.
"It's hard isn't it when you're not all together, being able to see them, muck around with them as well," sympathised Kate.
"We've got children the same age as you and a bit younger," said the Duke.
Told Ciara had learned about the Greek myth Pandora's Box that day, they laughed as she remembered the moral of the story, saying: "If someone says don't do it, don't do it."
"But there was also another message which was really lovely, do you remember?" added Fiona. "Even though there are bad things…"
"There's always hope," said Ciara.
"That’s very true," nodded William. "That fits very well with what we're all going through at the moment, does't it? There's hope ahead."
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