Hudson was born on 19 November 1990 in a small village in West Midlands, England. She is the daughter of journalist and author Cressida Connolly and Charles Hudson, of Wyke Manor. Cressida, who has written for Vogue, The Daily Telegraph, the Spectator and The Guardian, is the daughter of author Cyril Connolly, and great-granddaughter of James Craig, 1st Viscount Craigavon; she was previously married to Sunday Times and Tatler writer and critic AA Gill. James Craig, 1st Viscount Craigavon was married to Cecil Craig, Viscountess Craigavon, a great-great-granddaughter of John Bowes, 9th Earl of Strathmore and Kinghorne and Mary Bowes, Countess of Strathmore and Kinghorne, who were also the great-great-great grandparents of Lady Elizabeth Angela Marguerite Bowes-Lyon, mother of Elizabeth II. As such, Nell Hudson and Elizabeth II are fourth cousins, twice-removed. Charles Hudson, the son of Rosalind Hudson, was formerly the chairman of the Conservative Association of the South Worcestershire constituency.

Hudson’s first professional role, in 2012, was a guest spot in an episode of the fifteenth series of the BBC One medical drama Holby City. Later that year she appeared in Garrick Hamm’s short film Cast Offs and director Bruce Logan’s short Les Bohemes. In 2014, she landed the role of Laoghaire MacKenzie in Starz’s time travel drama Outlander, based upon Diana Gabaldon’s best-selling book series. The character is recurring and will continue throughout the series. On her character during the series’ mid-season episode, Hudson stated that “when you are in just a lot of pain, it comes out as anger… I think that’s quite a human characteristic, basically, and I think that’s definitely what happens is that she’s [Laoghaire] got all this pain and she doesn’t know what to do with it and it comes out in this very kind of aggressive way and she does whatever she can do to rectify the situation.”

Hudson guest-starred as Paulette Roland, a 17-year-old diabetic who discovers that she is pregnant, in series four of the BBC medical period drama Call the Midwife. The episode, which aired on 22 February 2015, explores the character’s struggle with the possibility of either a dangerous pregnancy or a legal abortion. That same year she guest starred in NBC’s international crime drama Crossing Lines. On 14 May 2015, Hudson played Lydia Bennet in Tamara Harvey’s production of Jane Austen’s Pride and Prejudice at the Sheffield Crucible, alongside James Northcote and Isabella Laughland.

In 2016, Hudson was featured in a series one episode of Sky1’s amateur detective series Agatha Raisin, based upon the book series by MC Beaton. Hudson also appears in ITV’s Victoria, a period drama centering on the life of British monarch Queen Victoria. She portrays Nancy Skerrett, the Queen’s dresser, in the ongoing series.