Welcome aboard, Jo!
The Western
Caribbean itinerary with Disney Cruise Line is one of my family's favorites. We've sailed to those ports of call quite a few times with Disney and have had fabulous and memorable experiences each time. I can't wait for you to experience these ports.
You will definitely need a valid UK passport for your cruise vacation, Jo, but you may also need Visas depending on which ports you visit. I don't believe you'll need it for your Mexican ports of call, nor Jamaica, Cayman Islands or Castaway Cay in the Bahamas, as it's mostly for ports in the Eastern Caribbean. However, please read a bit more about this on the
Passports and Travel Documentation page. I highly recommend that you call your travel agent or government agency in the UK to provide them with the list of the countries you'll visit to ensure that you'll have the proper documentation, as regulations change vary with each country, and I wouldn't want you to arrive without the correct travel documents, Jo.
Have so much fun planning your second adventure with Disney Cruise Line!
Marcy