If you are bringing 5 or less back per person - you only need the vaccination form which the breeder should provide - and the ring cards
DEFRA is not involved
1. “Pet birds” are considered to be all species of birds (except poultry as detailed below) which are accompanying their owners, or a natural person responsible for such animals on behalf of the owner during their movement, and are not intended to be sold or transferred to another owner.
5. 5 pet birds or fewer moved into the UK do not need to be accompanied by a licence, serve home quarantine upon arrival or have any inspection visits by a Local Veterinary Inspector (LVI).
6. Five or fewer pet birds may be imported per person, or a natural person responsible for the pet birds.
http://www.defra.gov.uk/animalh/int-trde/imports/iins/birds/a11.htm