This steep at times path runs along the east side of Summerhouse Plantation and through the red deer enclosure. With good views down of the red deer park and a small dew pond (photo below) as you climb.
Summerhouse Plantation is directly above the mansions car park. The recently restoration work has somewhat thinned the number of trees on its lower slopes since the above photo was taken.
From the mansion car park walkback toward the car park entrance until you reach a wide path running up the hill beside the fence of the red deer park.