This worked for me:

#!/usr/local/bin/perl

use strict;
use warnings;
use LWP::UserAgent::Determined;
use HTTP::Request::Common;
use Authen::NTLM;
ntlmv2(1);
 
my $url = 'http://www.bbc.co.uk/';

my $ua = LWP::UserAgent::Determined->new(keep_alive=>1);
$ua->credentials('www.bbc.co.uk:80', '', 'mydomain\\myuser', 'mypass')
+;
 
my $request = GET $url;
print "--Performing request now...-----------\n";
my $response = $ua->request($request);
print "--Done with request-------------------\n";

if ($response->is_success) {print "It worked!->" . $response->code . "
+\n"}
else {print "It didn't work!->" . $response->code . "\n"}

my $contents = $response->content();
print $response->status_line(), "\n";
print $response->headers()->as_string(), "\n";
[download]

Update: I couldn't get it to work correctly without setting $ua->env_proxy. Edited script to reflect that.
Update2: Last fix. Added ntlmv2 and decided to stick with the credentials method. Eliminated $ua->env_proxy; added my $contents