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Single-friendly cruiselines are: Crystal, Cunard, Fred Olsen, Holland America, Orient Lines, P&O & Silversea. Some have single cabins, others offer a reduced rate. It's worth shopping around as they really differ in price. Some even offer the chance to cabin share & have hosts on board to look after single passengers.
Very few, SAGA does but its prices in general are sometimes higher than other cruise lines but still cheaper than paying double, but you have I think to be over 50 to qualify for SAGA, but worth checking out a brochure.
Try Orient Lines Marco Polo, single occupied cabins usually cost 25% more but occassionally you can find a deal on Teletext with no single supplement, if you can go at short notice.