From the casework and style of the piano, I'd date it to the 1930s, which was an interesting and relevant time in the history of Pohlmann.
Pohlmann was an established maker based in Halifax, West Yorkshire. In 1934 the firm decided to close down manufacturing, and came to an agreement with Danemann of London to manufacture instruments on their behalf under license. All the patterns and templates to make the Pohlmann instruments were moved to the Danemann factory. Pohlmann kept their retail store and sold many of the Danemann manufactured pianos from there.
The case of your piano bears a striking resemblance to many of the Art Deco inspired pianos Danemann were known for pre-WW2, so if I had to bet on it I'd say yours was a post 1934 Danemann manufactured Pohlmann!
The other interesting thing to come out of the Pohlmann/Danemann arrangement was the rights Danemann acquired to use Pohlmann scale designs in their own instruments. As a young man, Henry Pohlmann was sent to study piano design in the Grotrian Steinweg factory in Germany. When he returned to Yorkshire, he came up with an excellent upright scale design which is likely to have been inspired by what he saw and learned at Grotrian Steinweg. This scale design was quickly incorporated into many of Danemann's own pianos, including not only uprights but the two large and well regarded grands designed by Peter Danemann in the 1950s.
(Info taken from "Five London Piano Makers" by Alastair Laurence, where more detail on Pohlmann and Danemann can be found.)
I found this blog post written by a tuner in Yorkshire which adds some fascinating additional detail on Pohlmann and Sons.
http://pianotuninginyork.blogspot.com/2 ... d.html?m=1