Can anyone tell me if it's possible to travel by ship from Turkey, preferably Istanbul to Egypt, Alexandria I would presume.

ohh. Is it possible to travel from Cypress to Istanbul by taking a ferry or boat? Any balloons travel from there?
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You can travel from North Cyprus (the Turkish controlled bit) to mainland Turkey by Ferry - but you won't be able to get from Egypt to Cyprus by sea

Re ferries from Cyprus to Egypt, yes, I made this journey.
They don't have ferries, but they do have different cruise companies.
I travelled from Turkey to Egypt via Cyprus using Salamis Cruises from Larnaca, Southern Cyprus.
I travelled from Mercin, SouthernTurkey to Northern Cyprus, via an over-night ferry, then crossed Cyprus, crossing the border into Southern Cyprus with no problem, and then from Larnaca, I booked through the Salamis Cruises company and travelled to Alexandria, Egypt where I disembarked.
Because the trip was part of a cruise trip however, it just meant that I had to request for permission to leave the vessel at Alexandria, which was also no problem.
It was very enjoyable, and I had my own cabin, the food provided, was exceptional and the price was very reasonable.