Cave was born 5 May 1987 in London, the second eldest of four siblings. Her father works as a general practitioner. Her grandfather was Chief Secretary of Hong Kong, Tasmanian-born Sir Charles Philip Haddon-Cave. Her younger sister Bebe is also an actress.
She attended Latymer Upper School in Hammersmith for sixth form. A former county-level swimmer and ex-national tennis player, she studied illustration and animation at Kingston University. Her tennis career was cut short by injury when she was 15. She had originally intended to study stage management at the Royal Academy of Dramatic Arts, and worked in London as a stagehand, before deciding to pursue acting.
Cave was previously in a relationship with Alfie Brown, son of composer Steve Brown and impressionist Jan Ravens. The couple have a son, Donnie (born October 2014) and a daughter, Margot (born July 2016). The couple's relationship inspired Cave's 2015 Edinburgh Festival Fringe comedy hit I Loved Her.
Cave made her acting debut in the drama Summerhill, shown on CBBC in early 2008.
Cave won the role of Lavender Brown in the film Harry Potter and the Half-Blood Prince through an open casting call held on 1 July 2007. Cave, who came from an agency, beat over 7,000 girls who turned up for the audition. She also performed the voice of Lavender in the video-game adaptations of Harry Potter and the Half-Blood Prince and Harry Potter and the Deathly Hallows: Part 2.
In June 2009, she made her West End début, playing "Thomasina" in a revival of Tom Stoppard's Arcadia at the Duke of York's Theatre. That December, Cave had a minor role in the 2009 film Inkheart as a water nymph.
Cave appeared in the play Breed at Theatre 503, playing the role of Liv, from 21 September to 16 October 2010. She won the Off West-End stage award for People's Choice for Female Performance.
On 4 February 2011, she appeared as a one-off character Hermione in the CBBC children's drama Sadie J.
Cave runs the website Pindippy, and its associated YouTube channel of the same name, which feature short videos written by and starring Cave herself, with occasional appearances from some of her other Harry Potter co-stars, including her close friend, Evanna Lynch.
During 2012, Cave played the title character in a 2012 production of J. M. Barrie's Mary Rose at the DogOrange Theatre, in London, Zazzy in the final episode of season 2 of Grandma's House, aired on 24 May 2012, and the role of Elder Biddy in the 2012 film adaptation of Great Expectations, based on the novel by Charles Dickens, and directed by Mike Newell. During the filming of Great Expectations, Cave worked alongside her younger sister Bebe (who played the younger Biddy), and was also reunited with her Harry Potter co-stars Helena Bonham Carter, Robbie Coltrane, and Ralph Fiennes. By June 2012, Cave had amassed over 30,000 followers on her Twitter account.
That August, Cave made her debut at the Edinburgh Festival Fringe with her show, Bookworm, which is described as "a charming hour of character comedy and loving literary silliness inspired by the obsessive Potter fans" Cave encountered while starring in the Harry Potter films. In the show, Cave stars as the bossy leader of a book club named Bookworms United, whose sidekick is played by her younger sister, Bebe. Cave's character expresses her enthusiasm for topics ranging from Babar to Andre Agassi's autobiography through a combination of homemade props and shadow puppetry, which conceal the character's neurosis, and contrast with a subplot about an ex-boyfriend.
During 2013, Cave played a minor role as a waitress named Angela in a medieval restaurant in the second series of BBC Three's Pramface, aired on 8 January 2013. She appeared as Theodora Snitch, a character in YouTube's one-off revival of the TV series Knightmare; Denise in episode 2 of Coming Up Series 8; as Alicia Ferguson in the CBBC series Wizards vs Aliens, in the two-part episode "The Thirteenth Floor"; as Anne-Marie in series 2 of The Job Lot, and as Annie Maddocks in the E4 drama Glue in 2014.
Cave published a book of cartoons called Lovesick on 2 July 2015 through Ebury Publishing. These cartoons have also been made into a Greeting Card range published by Cardmix.
She later created a fashion range of colourful boho-chic harem-style pants, called "Cave Pants". She also does regular comedy shows at venues in Soho, London.