I don't know about a 'full English translation" but you can find a description of the contents here, along with descriptive catalog entries, translations of the rather unusual conjurations(exorcistic texts), and transcription of the necrology(list of the dead who were to be commemorated in the mass, comparable I suppose to the diptychs in Orthodox churches):

http://www.kb.se/codex-gigas/eng/Long/texter/

As you can see, the vast majority of the book is a compilation of quite typical medieval texts-the latin vulgate, the antiquities of Josephus, several relatively popular medical texts, a relatively popular local chronicle, and texts for monastic ritual use. This kind of large-scale compedium is relatively common in medieval manuscripts; after all it made a number of books more accessible and because bindings were usually done separately and quite costly it was easier and cheaper to not have all the books bound separately. So there's not actually much reason for a full English translation-most of the book's contents are already generally available at least in publication and frequently in translation(although some texts may be harder to get ahold of if they are mainly available academic publications) and people who want to know about this specific manuscript will probably find the catalog entries and online photographs more useful than any compiled translation since those actually talk about the order of the book, foliation, collation, layout, materials, textual variants or omissions, and so on.