The one-off performance will see a cast perform songs from four brand new musicals.
Giedroyc will perform in Fanatical, a romantic comedy set at a sci-fi convention written by Matt Board and Reina Hardy. She will play the conference organiser alongside Game of Thrones' Gemma Whelan, who makes her musical and West End debut. It will be directed by Lottie Wakeham with choreography by Tim Jackson.
Joan, by Gwyneth Herbert and Mel Brimfield, is about the life of Joan Littlewood and will feature performances form Quentin, Gwyneth Herbert and Ian Shaw.
Directed by Maria Friedman and choreographed by Drew McOnie, The Happy Prince will see opera singer Hal Cazalet perform alongside Sophia Hurdley and Alan Vincent.
Wigmaker is a modern fairy tale about a beautiful wigmaker with music and lyrics by Tony Award winner Douglas Hodge and a book by Bryony Lavery. Hodge will perform alongside Haydn Gwynne.
The cast will also include Alex Gaumond, Jos Slovic, Emmanuel Kojo, James Smoker and Daniella Bowen.
New Songs 4 New Shows will take place at the Lyric Theatre on 28 November.