My tandem friend got back to me with his opinion on your tandem and this is what he thinks.
Due to the fact that it has a Chater-Lea headset
he is of the opinion that your tandem was indeed built to order from the Chater-Lea Fittings catalogue.
The original owner could have ordered a set of fittings (lugs, bottom bracket, headset etc, possibly frame tubing too) and had it built up by a local workshop, or commissioned Chater-Lea to arrange all of this work and then deliver the complete frame to the original owner.
As stated before, and illustrated by the period adverts posted by @New Mexico Brant
above) , Chater-Lea didn't build frames themselves as such, but you could order a frame from them built to one of their numbered designs.
Apparently they produced two double gent's style tandems featuring your tubing configuration.
Here they are from the 1931 catalogue.....
View attachment 1793390
...you could order a 'Model 14', or a 'Model 12B'.
The only difference between them is the choice of a single-sided drivetrain, or a cross-over drivetrain.
Your example has a frame designed to accommodate a single-sided drivetrain as the cut-out in the chainstay shows, and if you zoom in on the above image, you can see this illustrated.....
View attachment 1793391
...from this detail I think it's reasonable to think that you have a tandem built to the Chater-Lea 'Model 12B' design.
Here are the specifications for that model.....
View attachment 1793392
Still no clue as to the actual builder, and chances are we'll never know, but you have a top quality machine nonetheless.,
(Images from V-CC library).