In the the General Election 0f 1918, the first woman MP to be elected was Constance, Countess Markievicz. She was elected as the Sinn Fein Member for St. Patrick's Division, Dublin. However, as a member of Sinn Fein and someone who had, incidentally conducted her campaign from a prison cell in Holloway Jail [never actually charged with any offence], she did not take up her seat at Westminster.
Constance was the sister of Esther Gore-Booth, Manchester suffragist and campaigner for women's rights.