It's "International Phonograph and Indestructible Record Company", they were pirated recordings mostly from Edison or Edison Bell originals. The company was incorporated in 1902 and sold in 1904 to a Mr Robert Foster of Liverpool until about 1907 when it disappeared.
When your copy of "The Complete Cylinder Handbook" arrives, it has all the known issues of International Indestructible. They are of course only 2-minute cylinders.
Keith Harrison's "The Ultimate Phonograph Cylinder Handbook" arrived yesterday. What a super book that you, at The City of London Phonograph and Gramophone Society Ltd., have produced! I look forward to collecting others in your Reference Series.
Thanks for your kind words. If you are interested in obscure British cylinder manufacturers then RS23 "British Cylinder Manufacturers" and RS24 "The Pirates" may be of interest. They both include a well-filled CD of rare recordings and are only a fiver each.