The farmers' union has called on the government to place tighter controls on imports of foreign turkey meat, following the outbreak of bird flu.
A cull of 160,000 birds was carried out in Suffolk last week
Officials believe products from Hungary may have caused the outbreak at a Suffolk farm, but Hungary has said there was no evidence of a link.
The Food Standards Agency is investigating whether turkey products in supermarkets could be infected.
The government's chief scientist warned that meat may have to be recalled.
The FSA said it would not rule out a recall, but moved to reassure consumers that infected turkey would pose no risk to human health if the meat was properly cooked.
Richard MacDonald, of the National Farmers' Union, said the outbreak at the Bernard Matthews plant in Holton "posed questions about import controls".
He said he had asked the Department for Environment, Food and Rural Affairs "to examine very carefully what they do in terms of import controls and whether or not we should be continuing with this sort of practice".
Hungarian officials said there was no evidence to prove that infected poultry from Hungary caused the UK outbreak.
Hungary's deputy chief vet told the BBC he still believed that wild birds may have carried the virus to the UK.
1 Feb: Vets called to Bernard Matthews farm in Suffolk after turkeys die
3 Feb: Vets confirm H5N1 strain
5 Feb: Environment minister says most likely cause is from wild bird, but other possibilities being investigated
8 Feb: Government vet suggests turkey meat from Hungary may be to blame. Bernard Matthews denies link
9 Feb: FSA examines whether infected meat may have entered food chain
The European Union governs trade between its members but there are no restrictions on exports from Hungary.
A spokesman for the European Commission said "there is no immediate threat to Hungarian poultry or poultry exports" but non-EU members Croatia, Serbia and Russia have banned all poultry imports from Hungary.
Bernard Matthews owns the plant in Holton where the disease broke out, and also a site in Hungary.
The Eastern European country had its own bird flu outbreak on a goose farm last month.
Questions are now being asked of Bernard Matthews' conduct, after it emerged that the firm had been shipping partly processed meat from Hungary into the UK.
The NFU's poultry spokesman Charles Bourns played down suggestions that turkey from Bernard Mathews' infected farm may have ended up in the shops and restaurants.
"Those turkeys were eight weeks old. They were thirteen weeks away from the food chain. So there's actually no danger of any of them arriving in the food chain.
"And we're happy as farmers with what Defra have done, and we believe that they've now contained the disease on that one farm," he told BBC News.
FSA COOKING ADVICE
After cooking a whole bird, pierce the thickest part of the leg with a clean knife or skewer. The juices should run clear
The juices should not have any pink or red in them and there should be no pink meat
People are advised not to eat raw eggs or use raw eggs in dishes that will not be cooked
Eggs should be cooked until the whites are solid
Environment Minister Ben Bradshaw said the government was looking into whether there had been "biosecurity breaches" at the Holton plant.
Bernard Matthews denies any wrongdoing, but has stopped the importation of meat from Hungary while officials investigate the cause of the outbreak.
Bart Dalla Mura, commercial director of Bernard Matthews, said the firm had not brought any poultry or meat products from inside the infected region of Hungary into the UK.
"We have made all our checks and they have come from nowhere near the restricted region. That is what our paperwork says to us," he said.
Earlier this week, a cull of almost 160,000 turkeys at the Bernard Matthews plant was completed, after the discovery of the H5N1 virus.
The H5N1 virus does not pose a large-scale threat to humans, as it cannot pass easily from one person to another.
But experts fear the virus could mutate at some point in the future and trigger a flu pandemic, potentially putting millions of human lives at risk.