I continued to be intrigued by the pharma tyewriter and ended up doing some searching on Google and eBay (a useful source of comparison information) which let me know that examples such as this were pretty rare.
I ended up contacting Scott Kernaghan, a typewriter specialist and blogger, who was kind enough to take a look at my pictures and advise on a likely date:
I can tell you that it is was built between March 1922 – as that is when they started putting dual shift keys on this model, up until January 1925. Being that few models were made in that January, you can quite confidently say that the machine is from 1922 to 1924. That’s the closest I can tell you without the serial number.
When you have a chance to get a closer look at the machine the serial number should be found at the back right hand side of the machine.
Well, when I went to look for the serial number I found that the typewriter’s ninety five year old rubber feet had glued themselves to to an equally venerable rubber mat, meaning that getting at the serial number was going to involve a bit of delicate conservation work to unstick things, so I bailed out at this point, but still, to have a date of somewhere between 1922 and 1924 is pretty good …