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The nine-year-old off-spring is said to be "mad" about the British high street retailer and is glad she finally has the opportunity to wear grown-up clothes.
Kate's husband Jamie Hince told Grazia magazine: "She just loves clothes. She's mad about Topshop. Just before I left for New York, she was so made up because she could finally fit into the shop's petite range. But she was still a little bit devastated because there was so much she couldn't fit in to - yet."
It was recently revealed Lila enjoyed putting on fashion shows with her friend Iris Law, the daughter of Jude Law and Sadie Frost.
She said: "My god-sister, Lila, and I have gotten into the habit of creating little photo shoots every time we see each other. I enjoy this, because it's everything I love in one go; it's creative, it makes you think- it's fashion."