It appears that any birds that are Annex A,B,C on the CITES Species+ website will require an Export licence (£63) and you will need to obtain an Import Licence.
They will then have to go by special courier service to ensure all documentation is processed. The cost of this I am yet to find out.
This will mean that I am unlikely to be shipping Annex A,B,C species to the EU unless under special request. Howvere costs are likely to make this prohibitive.