It said it had finished culling operations at four premises identified as having had dangerous contact with the farm where the potentially lethal H5N1 strain of avian influenza was confirmed on Tuesday.
"Laboratory tests on samples from these premises are under way. There is no timetable for when the results will be received," the ministry said in a statement.
Approximately 28,600 birds were culled in total, including those on the original farm in the country of Suffolk.
The outbreak is the latest blow to the British farming industry this year.
Suffolk was hit by an outbreak of H5N1 at a turkey farm in February.
Some 159,000 turkeys were killed as a precaution. An official report said it was most likely the virus reached the flock via imported turkey meat from Hungary.
Britain's first foot and mouth disease cases since 2001 were found in August and the country's first ever cases of bluetongue disease in cattle soon after.