The ruins of the older house are evident here and there - you walk across the lawn and find you are in the old ballroom! If you put "Easton Cholmeley" in Google you can find out all kinds of things, including a pedigree of the Cholmeley family, a print of the original house (that's scary, when you have walked over the remains) and an account of a Cholmeley who died in the First World War. Franklin D. Roosevelt, the American President, spent his honeymoon at Easton Hall in 1903. What also happened was that the house was used as a billet by Allied troops during World War 2, and was demolished in 1951 due to being in a poor state of repair and needing too much spent on it. In 2000 the family started restoring the gardens, finding exotic trees and so forth which had seeded themselves. They now also promote their summer gardens, and hold painting days.
Here's a look at the old house - hope I haven't interfered with anyone's copyright:

Below: So where does this bit fit in? Obviously the stone staircase on the right is the highest one on the old picture. Behind where I am taking the photo there are other remains too.
Below: Taken from the left hand edge of the above photo, this one shows the sloping ground, which originally supported the terraced garden with the stone staircases.