I frequently cruise on my own. the cruise line that I use don't have single cabins, so i always pay a single supplement. It's usually 80% for inside and outside without balconies and 100% for suites and outside with balcony. I've found that if I try booking very early, the early booking discount helps offset it but often they say the higher grade cabins are not available (not sure if I believe them or whether they are retaining them for bookings of 2 or more) and sometimes when I have booked at the last minute, I've also got a very ggod deal and occasionally a better price. generally speaking some of the repositioning voyages work out more reasonable for a single person (if you don't mind lots of days at sea) Good luck finding something. As alwaays travelling on your own invariably costs more than if there were 2 of you splitting the cost but crusing is one of the best types of holidays for single people.
Several companies still offer single cabins eg SAGA, Fred. Olsen, P&O. Premia on double cabins can vary up to 70% but you can be lucky if the ship is not full.
Fred. Olsen Cruise Lines have world cruises from Southampton and Dover.
Apart from the one already listed Costa; Ocean Village; Viking River cruises all offer under 50% for the extra but others quoted inlcude Cunard; Holland America; Carnival and MSC. The is a 12 day cruise out of London on 25th July
Look on the web for single cruises and you will be amazed what is there.
P&O have one cruise on Artemis next year where there is NO single supplement.