That curved spoke-shave is specifically a Travisher, used in the main by chair-makers, along with a combination of an adze, gouges, compound-compass panes etc. to cut out the saddle shape on Windsor Chair seats. They are a bit awkward to sharpen and there’s a definite knack in using it………..
Possibly Brookes Brothers were the makers, though they could have been the suppliers who sold it; there is an extensive archive of Sheffield trade directories from the 19th and early 20th centuries, which should list where they were trading if you care to do a bit of research yourself.
I have looked in my books on saw and plane makers, which lists most of the tool makers that are known but there is only one very short listing for a firm called ‘Brooks Bothers’ who were saw makers in Sheffield from the 1860s.
If they used a Pike-staff as a trade-mark, as shown on your travisher, that may narrow it down a bit.