Because you never defined $ua, so the proxy call doesn't do anything. LWP::Simple doesn't provide an interface to set the proxies in this manner, you need to do it by setting the $http_proxy environment variable instead...

#!/usr/bin/perl -w
use strict;
use LWP::Simple

$env{http_proxy} = "http://myproxy:myport";

my $content = get("http://news.bbc.co.uk");

if($content) {
    print $content;
} else {
    print "Error: Get stuffed";
}
[download]