Find Your Cruise
I think there could be a couple of ways to do this.
One would be to find a specialist travel company that have group booked a number of rooms on a ship (lot of national and local papers advertise these types of holidays).
An alternative would be to contact a cruise line direct and ask the question.
As a single traveller myself I had the option to pay the single supplement or alternatively share a room when I went with Island, I chose to pay the extra however as I went in Oct the ship they waivered the single supplement and the room was half full anyway with a number of rooms free so I dont think anyone would have shared. Potentially therefore if you decided to book out or near the start/end of season even if you agree to share you might find you get a room to yourself anyway. One word of advice I would point out that shared rooms are typically offered on a same sex basis and no other spec so you could end up with anyone from a party animal to someone who snores and smells.
I think in this world climate it should be quite easy to get the single supplement knocked off and if your flexible on the dates you could even grap yourself a bigger better bargain. I booked initially for a week and then changed my mind and wanted to go for two. I got a price for 1 week then for 2. The 2 weeks ended up being cheaper than just the one week with all inc also in the package.
I dont know of a web site but I do know that a couple of cruise lines will take details and match up people who want to share. P & O certainly did it (last time I met someone in a shared cabin was 2007)and maybe princess also.