chomp $date;
$html =~ m{\Q$date\E(.*?)..............}ism;
[download]

Key components: chomp, quotemeta (or the \Q and \E metacharacters, and omitting the /g modifier, which isn't doing anything for you here (you're only matching once, and not in list context anyway).

Also, you're working to hard at printing your output file.

open my $HTML, '>', 'myhtml.html' or die $!;
print $HTML "$1\n";
close $HTML or die $!;
[download]

I don't think your content-type line is doing anything for you here unless you're creating a CGI script, in which case you probably wouldn't be opening an output file, but instead would just be printing to STDOUT (the default).