1. Sheffield is not in Germany, so therefore the audience were unlikely to be (a) aware or (b) offended. Singing that to a German audience is rather like singing The Sash in certain parts of Glasgow.
2. Small minded punks liked to use Nazism for shock value. They had nothing else to say except "Hey! We're over here! Look at us!"
3. Tomorrow Belongs To Me is totally irrelevant to this arguement since, as you point out, it's not a Nazi era song at all. He could just as well have sung Springtime For Hitler. What it became after Harvey sang it is even more irrelevant.
4. The lyrics were not hijacked by the Nazis, but instead accurately reflect the notions of romantic German nationalists in the pre-unification era, which overlapped with a large part of Nazi ideology. The first stanza is actually about Germany's natural borders (in their view), which would today require major redrawing of European borders.
http://ingeb.org/Lieder/deutschl.html5. The song itself wasn't aggressive enough for Mr H and friends, so the official Nazi anthem was the first stanza of das Deutschlandlied and then das Horst Wessel Lied, which instantly and permanently destroyed the credibility of the first part by association.