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Fred Olsen will have a lot of single cabins and they are costed at a favourable price.
You must be reading a different brochure to me. I think if you check again you'll find they are much more expensive than 2 people sharing.
If there are, I haven't found any, and have been sailing solo for 17 years. Have checked Fred Olsen prices but still find them a lot more expensive. I just have to bite the bullet and now pay up to 70% on P & O which is my favourite cruise line. PLease let me know if you find any.