Around 28,600 birds at the four sites have been destroyed after the farms were identified by Defra last week as 'dangerous contacts'. One site was later reclassified to 'slaughter on suspicion of avian influenza'.
Laboratory tests on samples from the premises were underway, Defra added, and the epidemiological investigation was ongoing.
Meanwhile, farmers could have to pay an extra £40m a year to the government to offset the costs of dealing with animal diseases, according to reports in the Daily Telegraph.
About £120m has been spent this year on tackling disease outbreaks and ministers hope they can claw one third of that back from farmers, the paper claims.