Curtis was born in London in 1995, and is the daughter of screenwriter Richard Curtis and broadcaster Emma Freud. In 2003 she made a brief cameo in her father's film Love Actually, playing Lobster Number 2 in the school nativity concert. She began her career as a blogger and has written for The Guardian, Elle magazine, The Times and The Telegraph. Curtis was the Sunday Times Style 'Gen-Z' columnist from 2016 to 2018.
In 2017 Curtis founded feminist activist collective The Pink Protest. The Pink Protest and Amika George organised the #FreePeriods campaign to fight period poverty. They have also campaigned with anti-female genital mutilation activist Nimco Ali to successfully include female genital mutilation in the Children's Act.