Gwynn and her future husband Harri Gwynn established a Plaid Cymru branch at the university, and was a member of Mudiad Gwerin ('the Peasant Movement'), which united nationalists and socialists. She was head of the physics department at Rhyl Grammar School between 1941 and 1942, before spending the remainder of the Second World War in Warwick and then London at the Government Exchequer and Audit Department as an assistant accountant. Gwynn had an ovarian growth removed and the experienced caused her to develop a dislike of using nuclear technology and nuclear power. According to Meic Stephens of The Independent, she was unsuccessful in other occupations because the interview panel had not expected to meet a woman and did not want to accept that one had a degree.