I came up with this code:

perl -n -e 'while(m/\b(DE\d{6})/g){print "$1\n";}' mypage.html
[download]

There is also this slight variation:

perl -n -e 'print "$1\n" while(/\b(DE\d{6})/g)' mypage.html
[download]

but I prefer the first because as a general rule I don't like suffixing statments with conditionals except for error handling.

It is slightly longer but does handle multiple matches in a line and it also breaks apart the output to one "DE" per line.