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You are covered by the ship's group visa for Egypt. You do not need a visa for Turkey if you arrive by cruise ship. Greece and Cyprus are in the EU so no visa needed there either.
British and Irish passport holders travelling to Turkey require a visa. Visas can be obtained at the port of entry or via the consulate before you go. Awaiting advise on Egypt, but no problems in Greece. I have a sneaky feeling we did not have a visa when we went in 2006 but we were OK as we went on a cruise organised outing.
UK citizens must have a valid passport, and a visa is required. A 30-day visa can be obtained on arrival for US$15 or the equivalent, provided the purpose of travel is for tourism. For travellers entering Egypt via South Sinai and remaining in the South Sinai resort area, a free 15-day visa can be obtained on arrival.
Passport/Visa Note: Passports must be valid for six months beyond the period of visit. Visa and passport validity requirements change at short notice.
Hope this helps.
More on Egypt but it depends where your cruise ship takes you:
British and other EU nationals travelling to Sharm El Sheikh, Dahab, Nuweiba and Taba resorts only, for up to 14 days, do not require a visa, they shall receive a free entry permission stamp upon arrival.
If you intend to travel out of the mentioned areas or overstay, you must obtain a visa.
Kindly note that your passport must be valid for at least 6 months from the date of travelling.
Turkey require a visa if you FLY in. Cruise ships are exempt.
Does this still apply for this year of 2012 please?
Well we've cruised three or four times to Turkey, Greece and Egypt and never had to get our own visa...they have always been arranged by the cruise company. The only time we did it ourselves was when we joined a ship at Sharm el Sheikh. Personally I would ring Royal Caribbean customer service and ask them if they arrange things like that for you.
Greece is in the EU so no visa needed. Been to Turkey (Kusadasi) twice in the last 2 years and did not need a visa. Been to Egypt (Port Said for Cairo) with P&O and an Egyptian immigration officer got on the ship in Malaga and stamped all passports. No charge.
Do not purchase a Visa for Egypt. I went through this performance 6 months ago & got differing stories with every telephone call I made! The cruise ships are granted a 'Block Visa' for their visit. You will receive a Visa, delivered to your cabin about 48 hours before arrival in Egypt, free of charge. There are No Visa's Required for any of the Countries you mention providing you arrive by cruise ship. Different rules apply to some Countries if you arrive by air.