Pankhurst was born on 19 June 1885 in Manchester, England, into a politicised family: her father, Richard Pankhurst was a socialist and candidate for Parliament, and her mother Emmeline Pankhurst and sisters Sylvia and Christabel were leaders of the British suffragette movement. Her mother was of Manx descent. Adela attended the all-woman Studley Horticultural College in Warwickshire, and Manchester High School for Girls.
As a teenager, Adela became involved in the militant Women's Social and Political Union founded by her mother and sisters. In November 1909 she joined a protest that disturbed a talk by Winston Churchill at his constituency in Dundee. She was arrested along with Helen Archdale and Maud Joachim. Adela had slapped a policeman who was trying to evict her from the building.
Eagle House near Bath in Somerset had became an important refuge for suffragettes who had been released from prison. Mary Blathwayt's parents planted trees there between April 1909 and July 1911 to commemorate the achievements of suffragettes including Adela's mother and sister, Christabel as well as Annie Kenney, Charlotte Despard, Millicent Fawcett and Lady Lytton. The trees were known as "Annie's Arboreatum" after Annie Kenney. There was also a "Pankhurst Pond" within the grounds.
Adela was invited to Eagle House in 1909 and 1910. She planted a Himalayan Cedar on 3 July 1910. A plaque was made and her photograph was recorded again by Colonel Linley Blathwayt.
Her mother's favourite was Christabel and the two of them took the Women's Social and Political Union as their own organisation. They fell out with many of their leading volunteers and supporters and this included Sylvia Pankhurst and Adela. Both of them believed in socialism whereas Emmeline and Chistabel were pushing for the vote for middle class women. Sylvia was ejected from the party and she set up her own splinter group in East London. Christabel is reported to have said to Sylvia "“I would not care if you were multiplied by a hundred,but one of Adela is too many.” Adela was given £20, a ticket to Australia and a letter introducing her to Vida Goldstein.