He made the one-off trip after nine-year-old pupil Beatrice Delap wrote to the star asking for help staging a 'mutiny' against the teachers, as he was filming at the nearby 18th century Old Naval College.
Ahoy there: Johnny Depp meets nine-year-old Meridian Primary School pupil Beatrice Delap and shows the letter she wrote asking him to help 'budding pirates' with their 'mutiny' against teachers
Budding pirate: Beatrice Delap
The school was told just ten minutes before that Depp would be arriving and two blacked-out cars swept through the school gates.
An onlooker said she heard the most 'incredible screams of joy' as the actor, in full make-up, then entered the school.
In an interview on London Tonight after the visit, Beatrice revealed what she had written in the letter to the star - or rather his salty seadog alter ego.
She said: 'Captain Jack Sparrow, At Meridian Primary School, we are a bunch of budding young pirates and we were having a bit of trouble mutiny-ing against the teachers, and we'd love if you could come and help.
'Beatrice Delap, aged nine, a budding pirate.'
She said that she was then asked by the star to make herself known from the assembled pupils once he arrived, and gave her a cuddle.
Beatrice marvelled: 'He gave me a hug and he said, "Maybe we shouldn't mutiny today 'cos there are police outside monitoring me."'
Police have been a constant presence as filming has progressed at the old college, parts of which have been transformed to look like Georgian London.
Depp has been seen filming scenes in which he jumped from a third-floor window and later balanced on a chariot pulled by galloping horses.
watch video here http://www.bbc.co.uk/news/entertainment-arts-11494594