Fred Landeg, deputy chief veterinary officer, said the cull was part of measures to contain the outbreak.
He said the virus was found in only one of 22 turkey sheds at the farm, owned by Bernard Matthews PLC, Europe's largest turkey producer.
Also on Saturday, WHO confirmed that bird flu killed a 22-year-old Nigerian woman, making her the first known human fatality of the H5N1 virus in sub-Saharan Africa.
Laboratory tests in London confirmed the findings of Nigerian health authorities, who announced on Wednesday that the woman had died after catching the virus from infected chicken.
The H5N1 virus has spread to 17 of Nigeria's 36 states over the past year despite measures such as culling, quarantine and bans on transporting live poultry.
Fears of pandemic
Bird flu has killed or prompted the culling of millions of birds worldwide since late 2003, when it began to affect Asian poultry stocks.
Experts fear it could mutate into a form that spreads easily among people, potentially sparking a global pandemic. Most human cases have been traced to contact with sick birds.
"This virus is going to be in bird populations for years to come, and the way in which we'll deal with it is by implementing the well-rehearsed plan to stamp it out at source"
Dr David Nabarro, UN flu co-ordinator
The English outbreak is the first known instance of H5N1 in Britain since an infected wild swan was found in Scotland in March last year.
Veterinary authorities were enforcing a 3km exclusion zone and a 10km "low risk" surveillance zone around the infected farm.
The European Commission said EU food and animal health experts would discuss the outbreak on Tuesday and review British measures to contain the disease.
The mass outbreak of H5N1 in Britain comes after Hungarian officials killed thousands of geese last month, on discovery of the virus in bird stocks in the southeast of the country.
Dr David Nabarro, UN flu co-ordinator, said experts had anticipated commercial flocks in Europe and elsewhere could be infected by migrating wild birds during the northern winter months.
"This virus is going to be in bird populations for years to come, and the way in which we'll deal with it is by implementing the well-rehearsed plan to stamp it out at source," he said.