Richardson was born in London, the daughter of the late director and producer Tony Richardson and actress Vanessa Redgrave, and granddaughter of the late actors Sir Michael Redgrave and Rachel Kempson. Her sister is Joely Richardson. She is also the niece of actress Lynn Redgrave and actor Corin Redgrave, and cousin of Jemma Redgrave.

Richardson made her film debut at the age of four in a film directed by her father, The Charge of the Light Brigade (1968). She attended St. Paul's Girls' School for several years, and then trained at London's Central School of Speech and Drama.

Richardson began her career in regional theatre, at the West Yorkshire Playhouse in Leeds, England. Her screen debut in Every Picture Tells a Story in 1984, was followed by a CBS miniseries, Ellis Island. A year later, Richardson appeared in a revival of Anton Chekhov's The Seagull; her first professional work in London's West End.

That same year she made her UK television debut alongside Jeremy Brett and David Burke in The Adventures Of Sherlock Holmes appearing as Violet Hunter in the episode "The Copper Beeches". Soon after, she starred in a London stage production of High Society, adapted from the acclaimed Cole Porter film, and successively portrayed Mary Godwin in the 1987 Ken Russell film, Gothic.

The same year she starred opposite Kenneth Branagh and Colin Firth in A Month in the Country, directed by Pat O'Connor. A major moment in advancement was her starring role in The Handmaid's Tale (1990), playing opposite Robert Duvall and Faye Dunaway. She starred in Nell (1994) alongside Jodie Foster and her future husband Liam Neeson.