Though an earlier building existed on the island, the present Duck Island Cottage, which is home to the Trust, was built between September 1840 and April 1841 and became the residence of the birdkeeper by 1870. However, by the death of the veteran Bird Keeper, Thomas Hinton, who lived there for more than 50 years until 1953, it was in a state of disrepair, not least due to air raid damage from 1940, and considered unfit for human habitation.
Having been saved from demolition, in 1959 it was remodelled and extended and became home to two more park keepers who lived there until 1980. In 1982 it was fully restored, and after a brief period as an office for the Bird Keeper and a store for confiscated bicycles, it finally became the headquarters of the London Historic Parks and Gardens Trust in 1994.
Today, it is still there and is still home to the Trust. It also has a lovely vegetable patch at the moment. For a full history, see here