I found your query by accident while looking up Balmforths of Leeds myself. My reason was because I have a viola which my Father bought from them in the late 1940s. At that time they were in the generous habit of giving away Hills of London bows, of which there were two qualities; 17/6d and 35 shillings. My father had one of the cheaper ones; I sold it two years ago for 1500 pounds!
Balmforths, however, no longer seem to exist, certainly not under that name