I've used the following solution before, which extends mechanize. I'm pretty sure I found this on perlmonks, but I can't find the original node, apologies to the monk i'm ripping off :)

#!/usr/bin/perl -w
my $mech = WWW::MechanizeCustom->new();
$mech->proxy('http','http://your-proxy:80');
$mech->set_basic_credentials( 'username', 'password' );


$mech->get("http://perlmonks.com");
print $mech->content;



#================================================================
package WWW::MechanizeCustom;

use base 'WWW::Mechanize';

# add a set_basic_credentials method, using a closure to remember
{
    my ( $username, $password );
    sub set_basic_credentials{ ( $username, $password ) = @_[1..2] }
    sub get_basic_credentials{ $username, $password };
}
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