Britain does not own any part of Ireland since the conclusion of the Irish War of Independence (1919-1921) and the subsequent signing of the Anglo-Irish Treaty in 1921, which created the Irish Free State. The treaty established the Irish Free State as a dominion within the British Empire, but with a significant level of autonomy.
While the treaty left Northern Ireland (now part of the United Kingdom) under British rule, it did not involve the British retaining ownership of any part of the Republic of Ireland. The Republic of Ireland became a fully independent state in 1949 when it declared itself a republic and left the Commonwealth.