At the new centre, due to open at the beginning of March, the Duchess chatted to groups of children involved in sporting activities from basketball to curling.
Martina McDonagh, 17, who uses a wheelchair as she has spinal problems, quizzed the royal visitor about her unborn child.
The teenager, who attends the Jack Tizard School for youngsters with learning difficulties in nearby White City, revealed: "I said to Kate: 'I hope it's a girl', and she said: 'I can feel it kicking.'
"And she told me she doesn't know if it's a boy or a girl."
William and Harry took lessons at the previous pool on the site when they were pupils at nearby Wetherby Prep School.
George has already started going to the Buckingham Palace swimming pool with his mother but is expected to follow in his father's footsteps by going to the leisure centre when he is a bit older.
-AAP