A horse-drawn carriage pulled the comedian's coffin, decorated with lilies, to the church in Bonnington.
Comedians Alan Carr and Jo Brand, and Rolling Stones' guitarist Ronnie Wood, were among friends and relatives in the congregation.
Dogs from Battersea rescue centre - where the TV star was an ambassador - formed a guard of honour at the private service.
This fan braved the wind and rain to pay her respects to the comedian.