The Exeter book is actually a collection of Anglo-Saxon manuscripts, and there is a copy in the original Old English lurking about, but it's a hard find and OE is as much like English as German is IMO.
However, if you look for the following, you should do okay:
Alexander, Michael (trans), The Earliest English Poems, London, Penguin 1991 (ISBN0140445943)
Crossley-Holland, Kevin (trans), The Exeter Riddle Book, London, Penguin 1993 (ISBN0140433678)
Raffel, Burton (trans) Poems From the Old English, Lincoln, U Nebraska P: 1964 (ISBN 0803251548) (Dr. Raffel was my professor's professor - I guess that makes him my "grand professor," though it also dates me considerably).