Workmen doing the piling for the foundations of the new footbridge over the River Haven, near the Stump, discovered the bones while drilling.
The Rev Alan Duce said: “The fact these were found 25ft down means they are very old. No one is buried as deep as that so the soil level has changed a great deal since the body was put there.”
He added: “We know that Botolph was buried somewhere near the site.”
Experts were being called in to examine the bones.