Okay, so it's not much of a secret, but it's hard to work out who it belongs to. There's a lot of big properties on Alma Road. I think this garden might belong to Laurel Bank, number 21, formerly Clark's Grammar School, apparently.
Interestingly, it seems that Clark's was a network of schools, including one not far from where I grew up in Ilford, on Cranbook Road. There's a website with some memories of the former Bristol school here, and one of the photos, titled "The Staffroom Window" is pretty much identical to my photo here.
I remember nothing of Clark's from my childhood, though they seem to be exactly the kind of place that my lot—Ilford County High—would have played cricket against, or something, so perhaps they got a mention in the occasional assembly.
GPS Coordinates:
51.46178, -2.61456
Location: Clifton