One of Glynne's main interests was mountaineering and rock climbing, although her family did not support the hobby, as her mother's cousin, Owen Glynne Jones died at the age of 32 in a climbing accident on Dent Blanche. Despite this, Glynne climbed throughout her life, including in Australia and New Zealand whilst she was touring there. She recorded the second ever ascent of Mount Spencer in New Zealand, the first by a woman. When she returned to Europe, she climbed major Alpine peaks such as Matterhorn, Mont Blanc, La Meije and Aiguille du Dru in the 1930s. She carried on climbing into her 60s, ascending Mount Fuji in Japan in 1963.