British Airways World Cargo, or rather, IAG Cargo as we call it nowadays, would be delighted to help you. There are various specialist cargo handling services on offer according to your specific needs and budgets. Please have a browse through the website and either drop the sales team an email or pick up the phone and talk to them. Yes, you will need to use a Freight Forwarder to do the customs paperwork and administrative nightmare bits for you, but we will gladly give you a list of forwarding agents. No difficulty is insurmountable for people trying to conduct honest business, I assure you!

https://www.iagcargo.com/iagcargo/portlet/en/html/main