Saint Edmund was first recorded in 1292 as 'Saint Edmund towards Garcherche'.
The original church was destroyed in The Great Fire and was rebuilt according to designs by Sir Christopher Wren in the 1670s.
The church was damaged by bombing during The First World War. Since 2001 it has been the London Centre for Spiritulaity and is still a consecrated church.
More information can be found on Wikipedia and from the Centre of Spirituality website.