Benet is a shortened form of the name Benedict. The benefactor who paid for the church to be rebuilt in the 13 Century was Robert Fink ( or Finch). A lane just off Threadneedle Street called Finch Lane is named after the same person. So the church was known a St Benet Fink.
The Church was founded by the Saxons in the 9th Century. The earliest written mention in a document is 1216. It was destroyed in the Great Fire of London in 1666, rebuilt by Sir Christoper Wren and finally demolished in 1846. A blue plaque on the wall of 1 Threadneedle Street has been erected in its memory.