Peake also told Maddison Webb, who is recovering after a bone marrow transplant to treat her acute lymphocytic leukaemia, about the need for restricted diets.
The patient at the Great Ormond Street Hospital (GOSH) received the long distance call of a lifetime when Peake took time out of his day on board the International Space Station (ISS) to speak to her in her isolation room at the hospital.
Peake and Maddison discussed being separated from their families and restricted diets during the call.
The astronaut told the youngster about the food he eats on the ISS as she prepares to eat food for the first time in more than a month.
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Her mother said: "Maddison has been in isolation at GOSH for five and a half weeks now and so she was very excited to speak to space from her room.
He also gave training tips after running the London Marathon using an on-board treadmill, as the hospital is encouraging people to take part in a 5K family fun run on May 15 in aid of the hospital.
After the call, that took place on April 28, Major Peake tweeted: "Thanks to the wonderful children & staff at @GreatOrmondSt for the great link-up yesterday. I loved sharing the #ISS & Earth views with you."
Last week, it was announced that the trio will return to Earth on June 18 - almost two weeks later than originally planned.