Speaking after their encounter, Ms Freeman told ITV: “It was really rather something, I’m so glad it’s happened.
“He’s kept up with his Scottish dancing but he says he doesn’t do so much at the moment as you can imagine, having not been too good.
“But it’s so lovely to see everybody turn out for him and he was looking very well, I thought.”
She revealed that during the King’s lessons, she would step in as his dance partner as she was a few years older and of a similar size.
She said he was a “talented dancer and very charming”, adding that she taught him the polka.
“It was very ‘au fait’ in those days,” she explained.
“You had to do the waltz, the foxtrot or this and that and the polka was quite fun for little ones.
“He was only four, Princess Anne was there but she was practically a toddler, it was a lucky and great privilege.”
The Vacani School of Dance, which was founded in 1915, counted Princess Elizabeth and her sister, Princess Margaret as former pupils.
Every week, Marguerite Vacani and her niece Betty Vacani would visit Kensington Palace and Windsor Castle to teach the royal children with the help of a young Ms Freeman.