What are the visa requirements to travel from the UK to the USA, on to the Caribbean and back to the USA?

To be quite honest the passport here won't matter much come to think of it.

The only way you will legally be able to do this as a visitor is by obtaining a B1/B2 visa from the US consulate at the country of your residence.

B1/B2 visa allows your stay up to a maximum of 6 months without an extension and can be extended(potentially). And visits to the Caribbean usually don't count as time out of the country see questions like:

• How soon can I re-enter the USA having stayed for 90 days under the Visa Waiver Program?

Presuming your cruise starts and ends at the same port (a "Closed Loop" cruise), then the time you are on the cruise would normally count against the 90 day period for the visa waiver program.

You can find additional information on the CBP website, with the relevant section being :

If you are traveling under the Visa Waiver Program (VWP), your I-94W (immigration stamp) that you were issued when you first entered the U.S. can be used for reentering the U.S. at the end of your cruise - as long as the cruise ends before your 90 day admission period has expired and you did not travel beyond adjacent islands or contiguous territory, and you were not outside the U.S. for more than 30 days. If the cruise takes you beyond that 90 day admission period, you will have to apply for a new admission, and you will have to convince the CBP Officer that you were not just taking the cruise in an attempt to circumvent the 90 day limit for VWP travelers.

(Note that I94W forms no longer exists in a physical form, but the concept is still the same - it's just all electronic)

It may be possible to convince the customs officer to give you a new 90 day period, but I would suggest that it's unlikely. It's also likely that you will have trouble with your airline not allowing you to board the plane for your initial trip to the US given that your return trip is more than 90 days out.

The alternative is not to use the Visa Waiver Program, but instead obtain a B1/B2 Visa, which will allow you to stay in the US for up to 6 months. Otherwise you could obviously change your travel plans to make the entire trip less than 90 days in duration - including the time on the cruise.