This is correct, the BOAC Argonaut routed London-Rome-Cairo-Aden, with a BA flight number out to Cairo, and a (completely different) AD flight number on to Aden. It appears to be the only service of the week from London to Aden - which was still a major port for British liners coming through Suez to Asia and Australia, and thus most of its connection was by sea. Aden Airways were wholly owned by BOAC, and leased their Dakotas from the parent company.
115/116 were indeed the BOAC flights to/from Johannesburg, also stopping at Rome and Cairo. The Comets operating this and other services had been grounded four weeks previously, timetables would have been in a flux and the printed documents probably in no way reflected reality - that Aden Airways timetable dated 1 May had probably been in circulation since before the grounding, and in those days likely went to print a couple of months before that. Reservations for those travelling from London to Rome and Cairo were also doubtless in a mess, which would upset the Aden flight.