The tune from the German National Anthem is actually part of Haydyn`s `Kaiser Quartet`. However, as with so many other good tunes, it was simply appropriated as a suitable tune for an english hymn as well, and appears in The English Hymnal and several other collections. It was, however, generally avoided during WWII for obvious reasons.
Of course, the Germans had a good selection of home grown music to choose their hymn tunes from, whilst english composers` music was not only less prolific, but also tended generally to be a bit less adaptable, with, of course, a few notable exceptions.