Anna Chancellor, who is best known for her role in Four Weddings And A Funeral, paid tribute on her daughter's Instagram page, sharing a picture of her as a young girl.
She wrote: "On September 29th Poppy died, held tight by her immediate family just as she had wished. Despite every effort, her body could not continue any longer."
Thanking the medical staff at the Royal Marsden, where Poppy was cared for, she went on: "We, her family and friends who all adore her join the other families who have lost their loved ones far too young.
"We continue to pray and support her in any way we can to further her soul's journey.
"Poppy was and is an unbelievable life force of creativity, compassion, wit, beauty and sheer uniqueness. She transformed our lives and we are beyond grateful."