It's an unusual chair - PC-rockers don't seem to come up very often - and this one is particularly nice as it appears to have it's original rockers. Their shape is similar to the fancy frieze that Clissett used on many of his spindlebacks.
Unlike the other rockers illustrated on this website, this chair is based on Clissett's simpler (cheaper?) range of chairs
This chair also solves a small problem in that I've never had my hands on a Clissett rocker, and wasn't sure of the dimensions. They all appear to have taller backs than standard side chairs. Now, thanks again to Bamfords, I have some dimension. This chair, at least, is the same height as Clissett's standard side chairs - quite small at about 34 inches (87cm). But the seats are lower, and the backs therefore taller - seat height is about 13.5 inches (34cm). This is very similar to a little 4-rung ladderback, which appears to be a nursing or child's chair.
So these little rocking chairs, along with the 4-rung ladderback, seem to be a specific class of chair amongst Clissett's standard range. Are there any full-sized Clissett rocking chairs out there, or any ladderback rockers? Do let us know.
You can see this new chair alongside all the other spindlebacks here.