Kirby's early television work included guest appearances and supporting roles in British television series. This provided her with valuable experience in front of the camera.

Appeared in an episode of BBC's "The Hour".

Appeared in an episode of ITV's "Agatha Christie's Poirot".

Starred in the BBC Two adaptation of Ronald Harwood's play "The Dresser".

Kirby achieved widespread critical acclaim and international recognition for her portrayal of Princess Margaret in the first two seasons of Netflix's "The Crown". Her performance earned her a BAFTA Award for Best Supporting Actress and solidified her status as a major talent. She left the series after season 2 as the character was recast to reflect the aging of the Royal Family.

Starred as Estella Havisham in the BBC/FX miniseries "Great Expectations", an adaptation of Charles Dickens' novel.