Hi Fensome, yes 3 people can share and generally the 3rd person doesn't pay as much. Shop around, check dates and availability with cruise.co.uk and other agents for best prices. Be careful of booking carribean in the summer months (hurricane season.
Many cruise lines have 4 berth inside cabins depending on where you want to go will determine what the 3rd person sharing will pay - it can vary anything from 40% to 80% discount and on odd cruises can even be free. An example of this is P&O Aurora Jewels of the Adriatic 20th April - 6th May the 3/4th person sharing goes free.
I would suggest you speak to a specialised cruise agent as some 4 berth cabins have upper pullman berths and I dont think these would be suitable for you. P&O have some super cruises and many of them sail out of Southampton thus avoiding the hassles of airports. They have some lovely ships and are very good value for money. Happy Cruising.