There are 3 St. Botolph's in London, and this one appears to be:
St Botolph-without-Bishopsgate is a Church of England church in the City of London, dedicated to St Botolph. It is situated outside what was Bishopsgate, about a 2 minute walk from Liverpool Street station. Adjoining the buildings is a substantial churchyard and former school. It is linked with the Worshipful Company of Bowyers.
Christian worship on this site may have Roman origins, though this is not fully proven. The present church (the fourth on the site) was completed by George Dance the Elder in 1725, the previous one having survived the Great Fire of London in 1666 only to be demolished in 1725. During construction, the foundations of the original Saxon Church were discovered.
The infant son of the playwright Ben Jonson is buried in the churchyard, and baptisms in this church include Edward Alleyn in 1566 and John Keats (in the present font) in 1795.
Here is the only photo I have found so far, and it is interesting that there is an image up on the second level on the back wall that is similar to the one in the ghost photo
It isn't in the same place, but makes me wonder if the ghost photo isn't showing something that is just part of the church. Anyone have time to pop over there for a look-see?