The locations were identified as having "dangerous contact" with birds on a nearby free-range farm that were confirmed as having the highly pathogenic virus on Tuesday.
Amid fears over the impact on Britain's traditional Christmas turkey trade, officials said the birds at the new sites were at risk of exposure to the disease due to the movement of people from the initial case.
"At this stage we have not confirmed disease on any of these four premises," said Britain's acting chief veterinary officer Fred Landeg.
"This is a precautionary measure taken to prevent any potential spread of the disease."
There are more than four million turkeys, chickens, ducks and geese registered within the 10-kilometre (six-mile) surveillance zone around the infected farm in the village of Redgrave, in the county of Suffolk.
The cull has raised concerns that there will be turkey shortages heading into the busy Christmas period next month.
All the major supermarket chains reported they had been unaffected so far by the situation and turkey sales had not dipped.
A Tesco spokesman said: "We haven't seen any change in buying patterns which shows that as expected, customers are taking a sensible view of the situation. There is no shortage of supply."
A Sainsbury's spokeswoman said: "The culling of turkeys on the additional four farms recently announced will not affect our supply of turkeys in the near future or in the run-up to Christmas."
Tuesday's sales figures showed no change to turkey sales, she added.
The cull at Redgrave involves some 5,000 turkeys, more than 1,000 ducks and 500 geese. About 100 turkeys were found dead on Sunday, and overnight between Sunday and Monday a further 80 birds died.
Landeg said the strain of virus found was closely related to strains discovered in Germany and the Czech Republic in the last six months.
The Food Standards Agency watchdog reassured consumers that poultry meat and eggs were still safe to eat, so long as they were cooked properly.
The new bird flu cases are the latest blow to the British farming industry this year.
Suffolk, a large poultry producing area, 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.