The case was found among about 9,000 turkeys that had just been culled at a farm on the border of Norfolk and Suffolk counties, the Department for the Environment, Food and Rural Affairs said.
The farm was one of several with turkeys, ducks and geese where culls were taking place because of fears of "dangerous contact" with the farm in the area where an initial case of H5NI was discovered last week, the department said.
All the farms where the culling was taking place are connected to the Gressingham Foods company, and the Department of Environment, Food and Rural Affairs was investigating whether H5N1 had spread between them.
Bird flu's return to Britain weeks before the Christmas holidays has been another blow to Britain's farmers, already struggling after livestock herds were hit earlier this year by foot-and-mouth and bluetongue.
The H5N1 strain was closely related to those found in the Czech Republic and Germany earlier this year.
Millions of birds worldwide have died or been slaughtered since late 2003, when H5N1 began ravaging Asian poultry stocks. It has killed at least 206 people worldwide since 2003.
Experts believe most victims were probably infected through direct contact with sick birds.
Bird flu is difficult for humans to catch, but experts fear it could mutate into a form that spreads easily among people, potentially sparking a flu pandemic.