Geldof married SCUM front-man Thomas Cohen at the same church in 2012. The site is also where her father wed her mother, TV host Paula Yates, in 1986, and where Yates' funeral was held after she died of a heroin overdose in 2000.
Geldof’s ashes were expected to be scattered in the garden of her home after the service.
Among the mourners at the funeral were Kate Moss, Sarah Ferguson, Nick Grimshaw, Bill Wyman and Jools Holland.
Geldof died April 7 at her home in southeast England. Officials have classified her death as "non-suspicious but sudden and unexplained."
An autopsy on her remains proved inconclusive, and the cause of her death will not be determined until the results of toxicology tests are complete in another week or two.