Baillieu was born in South Africa in 1982. Far from a child prodigy, he was encouraged to take up the piano after being diagnosed with poor hand-eye coordination. At first, he showed little talent but a great deal of enthusiasm, to the point where his mother had to tell him to stop practicing and go outside and play. He still claims to be unable to catch a thrown ball, however. Baillieu studied music at the University of Cape Town and turned to the role of accompanist when given the opportunity to work and perform with singers in the school's strong opera program, including soprano Pumeza Matshikiza. In 2005, he won a scholarship for foreign students at the Royal Academy of Music in London. Graduating in 2007, he won the Christian Carpenter Award and notched competition prizes in England and beyond. These included a win at the Das Lied contest in Berlin, where one of the judges, Annette Dasch, was so impressed that she asked him to work with her. Baillieu has been supported by the prestigious Young Classical Artists' Trust and has won several other important scholarships. In 2011, he was appointed professor of accompaniment at his alma mater, the Royal Academy. From 2012 to 2016, he held the prestigious Borletti-Buitoni Trust Fellowship.
Baillieu has collaborated with top singers, including Dasch, Ian Bostridge, and Kiri Te Kanawa, as well as instrumentalists such as the Elias and Heath Quartets. He plays several concerts a year as a soloist and has appeared with the Ulster Orchestra, the English Chamber Orchestra, and the Wiener Kammersymphonie. Baillieu made his recording debut in 2013, backing tenor Ben Johnson in Britten's The Canticles, and he has been sought out by singers for albums on the boutique Champs Hill and Resonus labels. He presented his own series at London's Wigmore Hall, accompanying a variety of top singers. In 2018, he joined both singers and instrumentalists for an album of music by Reynaldo Hahn on the Champs Hill label, and he backed trombonist Peter Moore on the latter's album Life Force. The following year, Baillieu was heard with violinist Tamsin Waley-Cohen on a Signum Classics recording of the complete works for violin and keyboard of Carl Philipp Emanuel Bach. The pandemic era saw Baillieu keep busy in 2021 with a pair of albums on which he accompanied clarinetist Julian Bliss and flutist Adam Walker. He returned in 2022 as accompanist to baritone Benjamin Appl on Appl's recording of Schubert's Winterreise, D. 911. ~ James Manheim, Rovi