Department for Environment, Food and Rural Affairs said it had no evidence that the outbreaks were caused by the introduction of infected poultry or poultry products, or that the disease was spread by wild birds. Neither possibility, however, could be ruled out.
"It has not been possible, at this stage, to categorically identify the source of the outbreak," DEFRA said in a statement. "Further surveillance, testing and epidemiological work on this outbreak is ongoing."
The outbreaks both involved the H5N1 strain of the virus, which world health experts are tracking out of fear it could mutate into a form more easily spread among people and potentially spark a human flu pandemic.
The discovery of bird flu in Britain rattled the poultry industry weeks before the Christmas holiday.
The H5N1 strain of the disease is difficult for people to catch. Experts believe most of the 206 people who have died of it worldwide since 2003 were probably infected through direct contact with sick birds.
Last week Health Secretary Alan Johnson warned that a flu pandemic was "one of the most severe risks" facing the country, telling lawmakers that he had signed an agreement to secure the delivery of enough flu vaccines to cover everyone in Britain.