Wrench attended Brisbane Grammar School, the Queensland Conservatorium of Music (with Nancy Weir)  and undertook postgraduate studies in Vienna at the Vienna Conservatorium and then at the Hochschule für Musik (with Michael Radulescu).
Wrench won 1st Prize at the Melbourne International Festival of Organ and Harpsichord 'Bach Competition' in 1985, the Audience Price at the 1989 St Albans International Organ Festival, 2nd Prize at the Dublin International Organ Competition in 1989 & 1990, and First Prize at the 1992 Carl Nielsen International Music Competition.
Wrench returned to Australia in 1991 where he became Lecturer in Organ at the Queensland Conservatorium. He appears regularly as a recitalist throughout Australia and Europe and has performed as soloist with the Adelaide Chamber Orchestra, the Australian Chamber Orchestra, the Queensland Philharmonic Orchestra, Queensland Symphony Orchestra, the Queensland Youth Symphony Orchestra, and the Canberra Symphony Orchestra.
Wrench was Director of Music at Christ Church, Vienna (1986–89) and at St. Mary's Anglican Church, Kangaroo Point in Brisbane from 1994-2012. In 2013 he was appointed Director of Music at Christ Church, St Lucia in Brisbane.
- 2012: Joy to the World (Christmas at the Sydney Town Hall); Move Records
- 2009: J.S. Bach Organ Sonatas, BWV 525–530, Garnisons Kirke, Copenhagen; Melba Recordings
- 2000: One Two One (20th Century Music for Trumpet & Organ); Move Records
- Review of Christopher Wrench and Piers Lane Concert
- "Canticum - Good Friday Musical Meditation".
- "Saint Mary's Church - Kangaroo Point".
- Musical Notes, Kawai Keyboard Series 2007 (MS Word)
- "Die Musiker in 2006 (The musicians in 2006)" (in German). 2006. Retrieved 28 June 2008.
- "Melba Recordings".
- Hamill, Steve (31 March 2014). "St. Albans International Organ Festival Past Prize Winners" (PDF). St Albans International Organ Festival. Retrieved 22 June 2014.[dead link]
- "Winners 1980-2013". Carl Nielsen International Competitions. Archived from the original on 22 June 2014. Retrieved 22 June 2014.
- "Director of Music - Christ Church St Lucia". Christ Church St Lucia. Retrieved 25 March 2016.
- "Joy To The World". Move Records.
- "Melba Recordings".
- "One Two One". Move Records.
-  at Melba Recordings