There are many.
You could call the 0800 number at the top of the page or look at the offers fro RCI, NCL, P and O. Fred Olsen all of whom sail from the UK.
Most travel agents can also provide you with the required information.
Others will, no doubt, let you know other shipping lines that sail from the UK such as Cunard!!
As well those lines mentioned by John other lines offering cruises from the UK include: Thomsons, Voyages of Discovery, Transocean Travel, other lines also make occassional visits to the UK i.e Azamara.
Fred Olsen and Page and Moy cruise out of Liverpool. Fred olsen from Greenock, Newcastle,Dover, Edinburgh, Southampton. Southampton has the most cruises leaving but Dover and Harwich are also busy. Different cruise lines use different ports. The following lines all cruise out of UK ports: Crystal Cruises ~ Cunard Line ~ Fred. Olsen Cruise Lines ~ Hebridean International Cruises ~ NCL Freestyle Cruising ~ P&O Cruises ~ Page & Moy ~ Princess Cruises ~ Royal Caribbean International ~ Saga ~ Thomson ~ Travelscope ~ Voyages of Discovery ~ Go to a good Independant travel agent that specialises in cruises to get help choosing which line may be most suitable bearing in mind where you want to cruise to, the price you can pay and the ambiance of the ship. ie formal dining and clothing or freestyle. Happy research. Hope this helps.