It seems it didnt take that long.This excerpt from the book "Jack Tar";Life in Nelsons Navy mentions it was a few minutes.
"The Drum and Fife Beat to Quarters,bulkheads were knocked away,the Guns released from their Confinement,the whole dread Paraphenalia of battle was produced,and after a few minutes of hurry and confusion,every man and boy was at his Post"