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That incident triggered concerns sport could become a target for more attacks in the region and India remains nervous after militants killed 166 people in an attack on Mumbai last November.
England's cricket team had pulled out of their India tour following the Mumbai attacks before being persuaded to return and complete the series after an independent security assessment.
"This was an incredibly tough decision and one we didn't take lightly," Adrian Christy, chief executive, said in the statement on Badminton England's website.
"After the Olympic Games, this is the most prestigious championships in the world but we were not prepared to risk the safety of our players, coaches and staff in what we felt could have been a very volatile environment.""GREAT REGRET"
Christy said the federation had also taken advice from the British Foreign Office and High Commission in India.
"We have been in constant dialogue with them over the past couple of days," said Christy.
"The conclusion is that safety is of paramount importance and therefore, with great regret, the team will be returning home immediately."Sehwag eyes Champions Trophy return
However, an Indian badminton federation official blamed the media for causing panic.
"They (England players) didn't want to go actually. They were called back by their government over security fears," Punnaiah Choudhary, Badminton Association of India (BAI) joint secretary, told Reuters.
"They were disappointed and so are we as organizers. A rumour (of the threat) was stretched by the media internationally."Australia complete crushing win to level series
The decision comes a day after the country's home minister and local police chiefs had tried to allay concerns following reports the championships could be targeted by militants.
A Badminton World Federation official said England were the only team that would be leaving.
"No other team has withdrawn or indicated a decision to withdraw," S. Selvam, BWF media and communication manager, told Reuters