The substitution of Packenham for Jackson in the lyrics of "The Battle of New Orleans" by Lonnie Donegan is a deliberate choice that reflects the song's narrative style and the historical context of the battle. While the song is set in the American perspective, it is important to note that Packenham was the British commander during the battle, and Jackson was the American commander. The substitution of Packenham for Jackson in the lyrics is a creative decision that adds a layer of humour and narrative depth to the song. It is a testament to Donegan's ability to blend historical facts with storytelling, creating a memorable and engaging piece of music that honours the bravery of both sides involved in the battle.
From Wikipedia