Fychan is originally from Anglesey, and is the daughter of the late Vaughan Hughes, a broadcaster, journalist and local councillor — and Angharad Anwyl.

[1] Heledd attended Ysgol Gynradd y Talwrn and Ysgol David Hughes and then studied History and Politics at Trinity College Dublin where she served as Education Sabbatical Officer at the Trinity College Students' Union, and later as Education Sabbatical Officer for the Union of Students in Ireland.

[2] After completing a master's degree in Medieval History at Bangor University, Fychan worked for the Plaid Cymru group in London.

[14] As MS for South Wales Central, Heledd Fychan called for a full investigation into the deaths of two boys after a police chase in Ely, Cardiff and the events following the incident.

She is further a member of the following cross-party groups: academic staff in universities, arts and health, autism, children and families, children in our care, clean air, friends of Ukraine, lung health, music, peace and reconciliation, poverty, public transport, school food, tourism, universities, and women.