The following complete code works fine for me:

use strict;
use warnings;
use LWP::UserAgent;
use HTTP::Request;
my $ua = LWP::UserAgent->new;
my $req = HTTP::Request->new( GET => 'https://api.flickr.com/services/
+rest');
my $response = $ua->request($req);
print $response->code . "\n";
[download]

And gives the expected "200" as output. LWP::UserAgent 6.02, HTTP::Request 6.00, LWP::Protocol::https 6.02, Mozilla::CA 20110914, perl 5.14.3 on Linux. Hope this is useful.