He was born on October 19, 1743 to Benjamin James Armitage and Lillian Harriett Armitage of the wealthy Armitage family and was a direct descendent of James Armitage, one of the founding members of the town of Maundbury.
At an early age he expressed an interest in books and learning so in 1752 he was sent to foster with his uncle Edward Armitage who was living in London to recieve a proper education. He attended the University of Cambridge from 1762 to 1768 but was thrown out before completing his post graduate for pursuing a course of studies "most unbecoming of a scholar."
He returned to Maundbury with some 300 books he collected while in London and set about his private studies. With his parents both perishing in a fire in their summer house in 1759, Hamilton was the sole heir of the Armitage Estate. In 1770 Hamilton founded the Maundbury Historical Society with friend Andrew Tompkins. Feeling that his duties were distracting him from his studies he turned full control over to Andrew.
Taking little interest in town affairs he was viewed by many as an "outsider" due to his English fostering though this sentiment faded after the Revolution as well as the allowance of usage to his personal library by some of the more affluent members of Maundbury. There were many rumors of "strange going-ons" in the late hours of the Armitage Mansion including seances and clandestine meetings though none of these rumors were ever confirmed.
He died unmarried with no heir leaving the rest of his wealth to his library with instructions for it to be of use to the entire town. Many of his personal affects were given to the Maundbury Historical Society while the rest were auctioned off, including the Armitage Mansion which was converted into a bed and breakfast called the Maundbury Inn in 1929.