Kate offered Demi-Leigh Armstrong, 5, from Ashford, Middlesex, a rattle for her friend.
“Do you want to give him this one?” Kate asked.
Demi-Leigh bluntly replied, “No”, before turning her back on the Duchess.
But by the end of the day Kate had won around the little girl, who is recovering from a kidney transplant operation after contracting a rare condition, HUS, that attacked her vital organs.
Demi-Leigh, helped give her a posy of roses and the Duchess wished her happy Christmas.
“But it’s not Christmas yet,” said Demi-Leigh.
“Bye then,” said Kate.
“Oh give me a hug first,” said the little girl, grabbing her leg, and the pair exchanged a thumbs up.