I'm going off London - take that as you will, but on this occasion I'm referring to my earlier suggestion. This is because the stone is relatively clean, suggesting a non-industrial location, and probably not too much of a conurbation either. The first Clean Air Act was in 1956, but I don't think it was until the late 1960s that there was any major effort to clean the soot etc from the outside of buildings. So if this picture dates from the late 50s or possibly early 60s, the buildings have probably never been particularly dirty.
And another thought about a possible location: in front of the building there's a drive, then a lawn sloping down to the road, with a large tree. The road itself is hidden by the wall on this side of it, but on the right hand side there are steps going down. It's possible that there's a ditch or moat immediately in front of the wall (as we see it), with bushes growing in it, and the grass in the foreground could be the bank on this side.
So what I'm wondering is whether we have our backs to a castle, some of the features of which were imitated in the building we can see. As Little Nell said (Reply #7), maybe it's "a Victorian municipal building masquerading as a castle".
For those of you waiting for my sun and shadows analysis, it's springtime (daffs on roadside, some leaves on tree but not that many), and the sun is relatively high producing quite strong shadows. So more or less middle of the day, meaning that this side of the building faces more or less east.
