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The singer, 41, said the gesture made her love the monarch “even more after that” as she had given the advice in such a “caring way”.
Jenkins is taking part in a number of celebrations over the Platinum Jubilee weekend, including performing at a special outdoor concert at Sandringham on Friday evening alongside The Military Wives Choirs.
Reflecting on her most treasured memory with the Queen, the operatic singer remembered a time she was invited to an intimate lunch at Buckingham Palace when she was in her mid-20s.
She explained that after the meal was served she panicked as she was given a large glass bowl of water and a selection of fruit which she had “no clue what to do” with.
Jenkins said: “I looked across at Her Majesty and sensing my unease she caught my eye as if to say ‘follow me’.
“I watched her take the fruit, wash it in the water and dried it off with the gauze.
“I was so grateful because she did it in such a caring way to save me embarrassment. I loved her even more after that.”
Welsh star Jenkins will also be seen in Sunday’s Songs Of Praise: Platinum Jubilee Special airing on the BBC.
Later that day, she will be among the celebrities to travel in decorated open top double decker buses for the decade-by-decade celebrations as part of Platinum Jubilee Pageant.
The singer, who has performed for the Queen on many occasions, said that knowing the monarch is watching her perform always makes it “more nerve-wracking”.
She added: “Singing for her means you really need to bring out your best performance.
“It doesn’t matter how many times I perform for her or meet her, whether it’s in front of thousands or just at a small dinner, I will never be blasé about it.
“It’s a huge honour and lovely to be asked.”
Jenkins also offered her congratulations to the Queen on her historic 70 years on the throne, adding: “You have done us all proud and I hope these celebrations showcase the deep love, respect & gratitude the nation has for you. God Save The Queen.”