The new case of the H5N1 strain of avian influenza was found on premises near the first farm on the border between Norfolk and Suffolk, north of London.
"The laboratory test results today highlight the importance of poultry keepers in the area being extremely vigilant," said acting chief vet Fred Landeg in a statement.
"It is essential they practice the highest levels of biosecurity and report any suspicions of disease to their local Animal Health office."
Last Tuesday authorities ordered the slaughter of more than 6,000 poultry at a site near Diss in Norfolk, in the latest blow to Britain's farming industry after outbreaks of foot and mouth and blue tongue disease earlier this year.