Thanks for all the offers of help. Starting with the thoughts in this response I have made some progress. I now have:

my $URL = "http://target.site.com/path/to/file.gz";

my $ua = LWP::UserAgent->new(
    agent =>
'Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.7.8) Gecko/20050
+511 Firefox/1.0.4'
);
$ua->proxy(['http'], 'http://my.proxy.server/proxy.pac');

my $response = $ua->get("$URL");
 
if ($response->is_success) {
    print $response->content; 
}

else {
    die $response->status_line;
}
[download]

I put in the proxy server, based on the automatic proxy configuration URL I use in FireFox for HTTP. Once I did this, the 500 error went away to be replaced by a 404 Not Found error!

I check the URL, by cut and paste into browser, so that is OK. And I also changed the URL to a different file on an FTP site and that works OK. So the problem appears to be HTTP specific. Any further thoughts? And am I using that proxy call correctly?

Thanks