Woolgar is the youngest daughter of Maureen (née McCann) and Michael Woolgar. Her brother Dermot is a barrister and her sister Claudia works in the arts in Ireland. Her early years were spent in New Canaan, Connecticut, before the family returned to the United Kingdom in 1976. Her father worked as an economist for many years and the family travelled to Kuwait and Sharjah. Her mother is of Irish heritage. She was educated at Mayfield Convent, Durham University, and then Royal Academy of Dramatic Art (RADA). At university she directed Murder in the Cathedral in Durham Cathedral, acted and was a member of the Durham Revue. She graduated from RADA in 1999 and on leaving did mostly theatre, particularly at the Royal Exchange, Manchest via goodreads