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Many cruises are termed "Fly cruises" for that exact reason! Most of these will start their itinery with "Fly UK to (Port of embarkation)" which could be anywhere in Europe, USA or Caribbean. Most cruises that board in the UK will be stated as "Cruise only." Some cruise lines such as Royal Caribbean and Celebrity will allow you to book the cruise only if you wish, and then it is up to you to make your own way to the Port of embarkation. This can sometimes be quite useful for cruises sailing from Amsterdam or Copenhagen for instance. Don't forget though, if travelling independently the ship will not wait for you if your flight is delayed, it will if it is part of the cruise package! Generally you will be much better off financially taking a flight inclusive deal to the USA or Caribbean ( even if it does feel that you are travelling in a sardine tin), but this may well not be true within Europe, where many cheap flights are now available from a lot of smaller local airports. Happy cruising.
Good advise given there but I must comment one of points. ALL cruises can be booked 'Cruise Only'. They may not advertise that fact, it's just up to you to ask for a cruise only quote.
Sometimes, Fly cruises, when offered as a late deal, are advertised as cruise only and you have to book your own flights - if that makes sense.