The parrot had been imported from South America, a region so far free from bird flu, the Department for Environment and Rural Affairs (Defra) said in a statement released on Sunday.
It is the UK's first confirmed case of bird flu since 1992.
Debby Reynolds, the department's chief veterinarian, said the parrot was probably infected while it was housed in the country's quarantine system with birds from Taiwan.
Tests conducted on the Taiwanese birds that had died were inconclusive, she said.
Defra said the virus was most closely matched to a strain found in ducks in China earlier this year but was not very similar to strains discovered in Romania and Turkey earlier this month.
The H5N1 strain has devastated poultry stocks in Asia and killed nearly 70 people in the region.
It now appears to be spreading westwards to Europe, carried by migrating wild fowl.
Birds in Russia, Turkey and Romania have all been found to
be carrying the virus - spurring international efforts to contain its spread.
Several countries have implemented mass culling programmes of wild birds and poultry stocks, while bans on the import of poultry have also been introduced.
Health workers in Romania carry
out a cull of poultry stocks
On Monday, Russian veterinary officials confirmed a new outbreak of the virus in the central region of Tambov, about 400km southeast of Moscow.
Although the virus in its current form is said to be hard for humans to contract, its genetic makeup has been changing as it spreads and scientists fear it could mutate into a variant that is easily transmitted between humans.
That, they fear, could create a global pandemic placing millions of lives at risk.
Experts from the European Union are due on Tuesday to discuss the introduction of a ban on imports of wild birds into the 25-nation bloc.
EU officials have so far resisted calls for such a ban, amid worries it could create a black market that would only increase the threat of infected birds being smuggled in.