In 1801, the Act of Union took away Ireland's parliament - which had limited powers - and gave full power over Ireland to the English Government. This was because the 1798 Rebellion convinced the English Government that the Irish might resist its rule again, and it wanted to prevent this. For the remainder of the nineteenth century, England fully ruled Ireland.
The majority of Irish people were not happy with this situation. In the early 1800's, Daniel O'Connell tried to convince England to give Ireland her Parliament back. However, England did not do this in his lifetime. Despite this, O'Connell was successful at winning certain rights for the majority of Irish people who were Catholic, including the right to sit in Parliament at Westminster.
In the 1873, a political party called the Home Rule League was set up, with Isaac Butt as its leader. It continued to try to win self-government for Ireland. Its aims were quite modest, and it did not seek full independence from England. After Charles Stewart Parnell was elected as leader of the Home Rule League in 1880, the party became more organised. The Home Rule Movement was a very important part of the progress towards Irish independence, which was eventually secured in 1921.