[Arran]

It looks like the finish is pretty tired, and it looks like something was spilled over it to cause that finish loss. I think that you, or someone else, will need to strip the old finish off and start fresh as it originally had a tinted finish which is near impossible to do spot repairs with. The veneer looks like it may be poplar, or some other cheaper white wood, not walnut, so Philco used a medium walnut tinted lacquer to make it look like walnut, you could strip it and do what they did, or try dying it, but lacquer is probably easier. 
Regards
Arran