Leung was born in Scotland to Kar Wai Li and Peter Leung, both of Chinese descent. Her parents are now divorced and she currently resides with her father (a native of Hong Kong), two brothers (one named Jonathan) and a sister (Violet). Her father runs a restaurant in Glasgow, as well as a wholesale business in Chinese cuisine. Besides English, Leung can also speak Cantonese and Mandarin. Leung attended Hamilton College, a Scottish private school in Hamilton, South Lanarkshire. She currently lives in London.

Leung's father saw an advertisement for a casting call for Harry Potter and the Goblet of Fire and suggested she try out. She waited for a total of four hours in line before she got in. Her audition only took five minutes and she heard nothing further for two weeks; she was then called for a workshop and thereafter got the part of Cho Chang. She was selected for the role of Cho after beating over 4000 other girls (including actresses Courtney Webb and Michelle Ang) in an open call audition in London for girls of East Asian appearance. She stated in an interview with the Daily Record that her Scottish accent probably gave her an edge in the casting room by making her stand out.

Daniel Radcliffe, the actor who plays Harry Potter, said he found Leung to be "awesome" and a "really amazing actress." Leung delayed plans to go to art college and university in order to film Harry Potter and the Order of the Phoenix. In the film, Leung and Radcliffe share an on-screen kiss.