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Yes you can, but they charge quite a bit extra. Some cruise lines are better and more suited to the single traveller and offer low or no single supplements on some cruised. I cruised the Norwegian Fjords in May and the supplement was only an extra £100. Watch out for offers on teletext. Fred Olsen often have good deals for single travellers and so does Orient Lines ship Marco Polo. Over the years I have payed so much in single supplements that I now only go on cruises with no single supplement or a very low one. Happy cruising
Very few ships these days have dedicated single cabins. Most shipping companies will sell a two bed cabin for single occupancy. Expect to pay 130% to 200% of the per person rate, although sometimes there's no supplement.