Lots of opportunities as many cruise ships sail from the UK to the UK from Dover, Southampton, Tilbury, Harwich, Newcastle, Leith, Liverpool etc etc. Surf the net for masses of offers.
For even more variety you can take Eurostar to Paris and there are connecting overnight sleeper trains to Barcelona,Rome and Venice which are all home ports for lots of cruises.
If you are looking to go to the Caribbean from GB, as far as I know there is only P&O which do direct sailings from Southampton to the Caribbean and back to Southampton, these are usually 22 or 23 nights, but some are of a longer duration. Best bet is to go to the P&O website and use the Cruise Finder facility. Good luck.
I notice that your question referred to a Caribbean port to port cruise and believe the only way you could do that is to take the QM2 to New York and then take a follow on Caribbean cruise and then take the eastbound return Transatlantic voyage. Sounds great but very expensive!
Princess Cruises - Crown Princess - 4 Apr 2017 - 5nts
Rome (Civitavecchia) : Kotor : Corfu : Rome (Civitavecchia)
Now from £489pp
View No Fly Cruises from Southampton >>
Click here to see offer
Princess - Pacific Princess - 26 February 2017 - 22nts
UK : Hong Kong : Sanya : Singapore : Phuket : Cochin : Mumbai : Dubai : UK
Now from £1699pp
Click to View Info Page>>
Princess - Pacific Princess - 07 February 2017 - 24nts
UK : Sydney : Papua New Guinea : Yap : Koahsiung : Hong Kong : UK
Now from £1999pp
Click Here To View More Princess Cruise Deals >>