Couldn't you just use simple substitution, for such a minimal task? I mean I am the first (or one of them) to decry using a regexp for HTML, but this situation may not warrant more.

my $newstuff = "<p>New HTML here!</p>\n";
open my $in, '<', "infile.html" or die $!;
open my $out, '>', "tempfile.html" or die $!;
while ( my $line = <$in> ) {
    next unless $line =~ m!<\s*/body\s*>!i;
    $line =~ s!(<\s*/body\s*>)!$newstuff$1!i;
} continue {
    print $out;
}
close $out or die $!;
close $in or die $!;
rename "tempfile.html", "infile.html" or die $!;
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...untested, but it seems about right...