Sorry there are NO pictures! I was too engrossed watching this bird through binoculars to even think about taking a photo.
It was sitting on the fence at around 5pm and remained there for 20 minutes or so. It was less than a foot tall, head and wings mostly mid-grey, breast a lighter shade with darker banding / stripes.
At first we thought it was an owl (a Little Owl) but it didn't have a facial disc like most owls do and it had no obvious ears, although its eyes were rather forward facing. It actually reminded me of falcon (perhaps a merlin) with its neck pulled in.
Ours was a suburban garden 2 miles from Edinburgh city centre and although we often hear owls at night I've never seen one.
Any ideas?