You can sing "any suitable hymn" as a breviary hymn. The US breviary has a bunch of English-language hymns, some familiar and some not.
If you're interested in singing the older Latin breviary hymns (in Latin or translation), there is actually a very good Anglican site for that: Chantblog Resources
has links to a bunch of posts on the "Office Hymns".
They are very beautiful, especially the ones for the morning that celebrate the Seven Days of Creation, and the ones that send you off to sleep at night with a blessing.