Fred Olsen and Cunard are the main Cruise Lines that cater for single travellers. The first being the cheapest option. MSC sometimes offer very good single fares, but this would usually involve having to fly to somewhere like Genoa to join the ship! Cabins are often sold on a single occupancy basis at the last minute when the cruise still has many cabins unsold. These can sometimes be picked up for around £100 per day. Go to any agents website and click on "Solo" cruises to view what is available at any one time. Happy cruising.
If it is any help. Just to add a cynical note to what I have previously said. The way to get the very best single fares on a cruise is to find the largest ship you possible can belonging to most underpatronised cruise company, going to the least popular ports of call, at the worst time of year. For example The Balmoral going to Le Harve, Guernsey and Vigo in February and leaving in two weeks time, would probably be as near as you can get to perfect for cheap singles fares in my opinion at the moment! Do you get the idea? The more of these factors you can include in your chosen cruise, then the more likely it is that they will offer reasonable single fares. As A bit of a guide Thomson are offering single places for under £700 for a week, and there are single cabins available on the Grand Princesses 12 night round Britain cruise for around £1000 at the moment. Both leaving within the month. Happy cruising.