Very late, but just for fun since I can't sleep anyway...
Solution #1:

   use strict;
   use warnings;

   $/ = "<br /><br />";

   while(<DATA>) {
      chomp;
      my @record = split(/<br \/>/);
      print "@record\n" if (@record == 3);
   }

   __DATA__
Name1<br />Address1<br /><br />Name2<br />Address2<br />URL2<br /><br 
+/>Name3<br />Address3<br />URL3<br /><br />Name4<br />Address4<br /><
+br />
[download]

and solution #2:

   use strict;
   use warnings;

   $/ = "<br />";
   my $i = -1;
   my @record;

   while(<DATA>) {
      chomp;
      if (/^$/) {
         $i = -1;
         next;
      }
      $record[++$i] = $_;
      print "@record\n" if ($i == 2);
   }

   __DATA__
Name1<br />Address1<br /><br />Name2<br />Address2<br />URL2<br /><br 
+/>Name3<br />Address3<br />URL3<br /><br />Name4<br />Address4<br /><
+br />
[download]