I've just had a chance to look at my copies of the PG Diary(s) for L Cohen as a London agent. They are not mentioned in the 1938 edition. The only edition that I have which lists importers specifically is 1948, and that does not mention L. Cohen & Sons Ltd.
However, S. W. Stent of 31, Ely Place, London EC1 are already named as agents for Pearson & Co (Chesterfield) Ltd in 1938.
Therefore, I am wondering whether the theory about the Cohen family not surviving the war is relevant. Did the business even carry on until the war?