Cobbe was born about 1884 and graduated from the School of Physic, Trinity College, Dublin in 1906. Coming to London he was house surgeon successively at St Mark's, St Peter's, the West London and the Westminster Hospitals. During the war of 1914-18 he was a civil surgeon at the Middlesex War Hospital, and then a surgical specialist in the RAMC. Cobbe practised throughout his subsequent career at Dover, where he was surgeon to the Royal Victoria Hospital and the Dover Venereal Disease Clinic, and medical officer to Dover College. He lived for many years at 6 Cambridge Terrace, but retired to 61 Salisbury Road, where he died in 1965 aged about eighty-one.