World cruise on Cunard, P&O or Saga is your best bet.
It is very unlikely that you will find a cruise that will depart the UK go to the Caribbean and then back again. You can sail one way on repositioning voyages, when a ship goes from Europe to the Caribbean or South Africa for the winter and then vice versa in the spring. If you want to go far afield with no flying, then a world cruise is your only option (either one cruise or combining 2) This will obvioulsy mean you would be away 80 or 90 nights and the price will be very expensive compared to 14night fly/cruis.
P&O have round trip cruises to the Carribean, South and North America from Southampton. Carribean round trip is usually around 22days. In the autumn and spring there are repositioning cruises where you fly one way and sail the other. These are usually 14day.