Its true there is a approved list, however that does not stop you having to satisfying a few conditions,
1. They most enter/leave through a BIP (a veterinary inspection point approved for the product you are sending-especially if sending by air)
2. Must apply for a licence from / notify the AHVLA {Animal Health and Veterinary Laboratories Agency }(these are in charge of export/import, they are part of DEFRA but you will find they have all updated information)
3. Veterinary inspection and completion of health checks of the birds or if eggs/chicks the parent stock within ten days prior to the shipment.
These are mininium requirements as far as I'm aware for the UK and I'm pretty sure there are no counties you can send to legally without doing what I've stated. As for approved list basically if the country your wanting to import from is not on the list ,your not going to get anywhere with AHVLA.
This is information I got of the AHVLA when I contacted them about sending half a dozen or so eggs within the EU last month, so it is up to date, and you can can't just send eggs to approved countries without filling these forms in.
Regards
PS
Always check directly with the relevant authority before engaging in the Inter-border movement of animals and animal products (so the AHVLA in the UK and USDA in the US). It never hurts to send an email to clarify a position.