The advert compared the £49m it costs to sponsor the England football team in the World Cup with the 60p a day it costs to sponsor a child in the developing world.
World Vision claimed the BACC had refused to clear the ad on the grounds that it was an unfair attack on football and said it was "shocked and extremely surprised" at the ruling. A new version of the ad, making no reference to the England football team, will now be broadcast.
A spokeswoman for the charity said: "We sought advice from the BACC at the script stage and produced the original advert in accordance with its guidelines."
But this version of events was disputed by the BACC. "We didn't impose this ruling to be difficult," said Kristoffer Hammer, editorial standards manager at the BACC. "Our guidelines apply to all organisations. But we felt the advert implied that the sum spent on the England football team was not money well spent."
Hammer said the BACC had given the charity clear guidance on how to proceed.
"We advised World Vision that it could run the ad if it got permission from the Football Association or, alternatively, that it could remove the reference," he said. "The changed advert has already been approved."
World Vision has put out a press release to highlight the BACC's ruling and claim that it had to spend more money to make the new version. But a spokeswoman admitted that the costs were minimal.
She added: "We tried to get permission from the FA, but it declined to comment. The changes meant we had to compromise our message. The ad is now not as strong as we would have liked."