I've been doing some digging around and hoping to find more about the mystery ship.
The box is definitely a more or less standard Basset-Lowke item.
This is an illustration from Derek Head's book on the B-L Waterline Ships.
You can see the distinctive "star" pattern in both pictures. This is the remains of a faded label on the bottom of the box. I've tried UV light but if there was any printing, it's long gone. Of course, if this model was the product of a rehab type operation backed by B-L, it's possible that it never got an "official" label and there was just a name and price written in pencil.
This does not mean that the model is from B-L but I'm convinced there's some connection. In the immediate post-war period, the B-L factory in St Andrew's Street struggled to meet customer demand so much model making was out-sourced both locally around the town and nationally. This resulted in many variations in the quality of the models ships being sold.
So far, I've not managed to follow up Roger's suggestion to visit 78 Derngate and browse the records. However a contact in the town museum agrees that Wenman Bassett-Lowke did get involved in much social work around Northampton and a rehab facility making models would be very much in his style.
The next step will be a visit to the town's Central Library and some digging in the Local Studies collection of documents and records. Then the Public Records office.
I may be taking this model ship collecting a bit too seriously....