Churchill sailed from Plymouth to Alexandria on the battlecruiser HMS Renown via Gibraltar, Algiers and Malta, then flew from Alexandria to Tehran via Cairo in Ascalon, an Avro York transport aircraft derived from the Lancaster bomber, modified for VIP transport with facilities including a bar, ashtray for cigars and an electrically heated toilet seat.
By November 1943, following the invasions of North Africa and Italy, the Mediterranean was considerably more secure than it had been in August 1942 when Churchill had also visited Tehran, on the way to Moscow. On that occasion he flew directly from Gibraltar to Cairo in Commando, a modified B-24.
[Issue 148 of Finest Hour] (http://www.winstonchurchill.org/publications/finest-hour/finest-hour-148), the Journal of Winston Churchill, has several articles about Churchill's extensive travels during the war.