In case you haven't been given enough Ways To Do It, my first thought was HTML::TokeParser::Simple:

use HTML::TokeParser::Simple;
my $p = HTML::TokeParser::Simple->new( file => 'test_data.html' );
my $t; #token;
my @text; 

#get all text between pre tags
while ($t = $p->get_token) {
   next unless $t->is_start_tag('pre');
   
   my $content;
   while ($t = $p->get_token) {
      last if $t->is_end_tag('pre');
      $content .= $t->as_is;
   }
   push @text, $content;
}
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I'm guessing this isn't the fastest approach... but hey, TMTOWTDI.