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The get function returns a scalar, and according to the documentation for LWP::Simple, you can check for success with defined instead of "while". Something like this (untested):

use warnings;
use strict;
use LWP::Simple;
my ($html, $url);
my $count = 0;
$html = get("http://localhost:8080/html.htm");
die "Couldn't fetch page." unless defined $html;

if ($html =~ m{<(a class=\"smallV110\" href=\"/)(.*?)\">} ) {
   $url = $2;
   print "$url\n";
   $count++;
   print "$count\n";
}
else {
  die "couldn't match";
}
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