Giedroyc grew up in Leatherhead, Surrey. Her father is Michal Giedroyc, a historian of Polish-Lithuanian descent from the princely Giedroyć family, who came to England in 1947. She attended Bristol University, where she first began making films.
Giedroyc married her first husband at 21, and had a son before divorcing. She remarried in 1998 to Sir Thomas Weyland Bowyer-Smyth, 15th Baronet, a BAFTA-winning production designer, with whom she has two children.
Giedroyc has directed several films, including Women Talking Dirty and Stella Does Tricks; she is best known for her work directing television dramas, which have included Wuthering Heights, The Virgin Queen, Oliver Twist, Fear of Fanny, Carrie's War, and three episodes of Blackpool.
In 2007 she was nominated, with Paula Milne and Paul Rutman, for a Best Drama Serial BAFTA Award for The Virgin Queen. In 2010, her directing work for the BBC television series The Nativity was praised by critics, although the story portrayed some controversial elements that caused debate between Christians due to its modern dramatisations of the birth of Christ.
Giedroyc directed A Study in Pink, originally filmed as a 60-minute pilot for the television series Sherlock, which was written by Steven Moffat. The BBC decided not to broadcast the episode because they wished to change the broadcast length to 90 minutes. However, the pilot was released on the DVD of the first series, and it proved to be slightly different from the final version. She has also directed BBC's The Hour and What Remains. Giedroyc directed two episodes of the 2014 Showtime horror television series Penny Dreadful.
On 12 August 2014, Deadline reported that Giedroyc would direct the upcoming biopic Mary Shelley's Monster. The film starred Sophie Turner as the famed Frankenstein author Mary Shelley, Taissa Farmiga as Shelley's stepsister Claire Clairmont, and Jeremy Irvine as Shelley's husband Percy Bysshe Shelley. The film has been described as "a story of youth that transcends time, a gothic romance, a love triangle that involves a dark passenger."
On 20 December 2015, Giedroyc directed the live television production of The Sound of Music, starring Kara Tointon as Maria, and her sister Mel Giedroyc as Frau Schmidt. The two-and-a-half-hour ITV transmission was the first musical to be broadcast live on national television in the UK, and had a cast and crew of more than 400 and 177 costumes.