Welcome, and I wish you much enjoyment with your grandfather's binoculars. A well executed 10x50, in good condition, can still be a pleasure to use today.
Ratal's post #3 notes the reason why it's been difficult to track down the provenance of your binocular: it was most likely made by one of a number of Japanese manufacturers that produced binoculars from the 1950s to late 1970s/early 1980s, but sold (rebranded) under one of several brand names. In the US the most famous of these were Bushnell, Swift (also sold in the UK) and Tasco (not to be confused with Tesco!) and in the UK there were the likes of Hanimex, Zenith, Prinz and others - some binoculars were sold under the Boots label. Japan at that time was the workshop of the world, much like China is today: products made in the PRC today are more advanced in design, but many (though not all!) binoculars made in Japan in those days are mechanically very sound.
One thing that may help a little with finding out your binocular's history are "JB" and "JE" marks/numbers which denote which manufacturer in Japan made the body (metalwork) and optics (glass). These can be quite tricky to find as they are often small and located in odd places, but if you can locate them, you should be able to tell where they came from. For instance: JB-45 means that the binocular was manufactured by Tamron, which is today a well-known camera lens manufacturer.
Good luck in your JB/JE search!
PS. putting my binogeek hat on: it'd be interesting to know which military model the civilian 10x50 5.5 degree was based on - from what I gather, many of the 7.3 degree 7x50s were based on US designs (Bausch & Lomb etc) but I can't recall a similar template for the 10x50 5.5 degree. But my knowledge of military binoculars, especially Japanese ones, is pretty thin.