John Redman Ltd goes back a little further than 1933. In the fall of 1928 it was located at 4 Cock hill Middlesex St in London. In 1956 it moved to the 123 (afterwards expanding to 125 and 127) Whitecross Street address, where it remained at least until the 1980s. The company produced (or at any rate sold) a multitude of models. I have an industry handbook from the late 1960s that lists more than forty distinct "imported pipes", a number of Buescher cobs, Wellbents, carved Tyrolean pipes, Stonehaven & Cherries etc, and finally 19 "London Made" pipes ranging from 12/6 to 60 shillings.
The British Empire Pipe Co. is more obscure still. It was formed in 1934 apparently to import Algerian briar to Malta, where it was then made into pipes, largely for export to the UK and other parts of the Empire. I suspect it was established to take advantage of what we would today call an enterprise zone in Malta, when tax concessions and import preferences were offered to attract the capital necessary to stimulate business formation and job creation.
When and how the British Empire Pipe Co. was associated with John Redman Ltd is unclear, at least to me. At a guess I would assume that it was the source of many of the pipes listed many years later under the John Redman name as "imported". In any case the British Empire Pipe Co. maintained a London address at 26 Cross street, which appeared in London phone books from about 1957-1967.