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Many of the newer ships have one half of the lift open to either the sea or the open inside of the ship so you may have to walk down the passageways to get to them and these passageways are not dark dingy places but bright and wide so there is probably less of a claustrophobic atmosphere than you would imagine.
My suggestion is that you write to Royal Caribbean, Cunard, and P&O and tell them your problem. All three cruise lines have ships coming in quite close to you in Southampton and you may get invited to view one or more of them, with luck. …. Neil
The only way a cruise liner can be viewed is via websites for that particular line. Corridors are endless, but great fun. They are not dark very well lit. Go on to photos. You will be able to see corridors on most cruise lines. Lifts? You dont have to use them, but after all the fab meals and calories consumed you may well want to. But burn off those calories and use the stairs! I couldnt too full! You will love it regardless!
There are some good sites with virtual tours of pretty well every cruise ship. Here's one http://cruises.travelnow.com/c/cruisemain.asp & for some of the best still pictures google Ship Parade (one word).
A ship such as Arcadia will be suitable.
The corridors are very well lit and there are open view lifts on both sides that face the sea.
If she suffers from small enclosed spaces DO NOT book an inside cabin and check the cabin sizes carefully. I went on NCL Jade this year and the cabin was tiny and with lower ceilings on ships, it makes it a claustrophobics nightmare.
I can only offer limited advice (based on Cunard), but I would suggest looking at the deck plan, and going for a midships cabin, meaning the longest corridor distance would be half a ship's length. Also, if you look for a cabin by one of the stairwells, then you could easily cover much of the distance through public rooms by perhaps just walking up a deck. For example, choosing a Deck 6 cabin on the QM2 would put you a deck below both King's Court and the Winter Garden, leaving virtually no corridors to cover.
The corridors on QM2 were very light and airy, as were the cabins.
Certainly worth speaking to the cruiselines and seeing if there is anything they can do to assist. Best of luck - I do hope you find something that you will both enjoy. It might be worth trying a mini cruise first - sometimes knowing that you have only 1 or 2 nights aboard can make the decision easier.