Re-visited this today and had a bit more of a nose around. I really doubt that this is, or was ever, a round barrow. It strikes me more as a ringfort or rath – it has that feel about it. However, there is a bank and ditch just a metre inside the tree/shrub-line so it could certainly be a flattened/robbed-out barrow.
It's situated above the mill road on a natural, defensible hillock and is on the grounds of Stewart's Hospital. There has been work carried out near it recently but it seems that due respect was given to the monument during construction.
The grounds of Stewart's hospital are a bit of a maze. I had to ask directions for this from a staff member. On the last day of November '06 in the wind and rain I didn't venture into the undergrowth to check the structure.