The 21-year-old is the current European champion and will be officially confirmed as the world number one on Friday, but GB Taekwondo instead selected world number 56 Lutalo Muhammad, apparently because Cook trains outside the official GB set-up.
A four-man team of BOA chief executive Andy Hunt, Sir Clive Woodward, deputy chef de mission Mark England and chairman of the BOA’s athletes commission Sarah Winckliss met on Tuesday and have since summoned GB Taekwondo for urgent talks.
"The OQS Panel is requesting a meeting at the earliest possible opportunity with the British Taekwondo Selection Committee," read a BOA statement. "With respect to the nomination in the Men's Under-80 kg weight category, we seek further information and clarification about the process by which the athletes were evaluated by the British Taekwondo Selection Committee.
"Once the OQS Panel has had an opportunity to ask further questions of and receive additional information from the British Taekwondo Selection Committee, it will be in a position to act upon the nomination."
The decision to leave him out has not been formally explained by GB Taekwondo, but it is believed to relate to Cook’s decision to follow a self-funded coaching programme rather than work within the framework of the governing body.
"I find it incredible as the world No 1 in my sport, I may not participate in the Games due to the ‘opinion’ of a committee," Cook said. "I do not want to be a precedent. I want the chance to win a gold medal for Great Britain. My whole career is at stake with this decision.
"I hope that this process never happens again to any other athlete in British Taekwondo or any other sport."
Cook competed for Britain as a 17-year-old at the Beijing Olympics in 2008, and has subsequently improved. He has been ranked in the top 20 for the past two years, and has been number one for 13 months in that period.
Muhammad, who took Cook’s place in the four-man squad, is also a European champion, but not at the -80kg weight category. His -87kg triumph was at a weight which is not contested at the Olympics.
He is highly regarded as a prospect, but while he has yet to win an international event at the -80kg category, Cook has won nine in the past year.
GB Taekwondo have insisted that their selection for London 2012 was based on "expert judgment".
"The selection panel’s primary aim has always been to select athletes who have the best potential to win the best set of medals for Great Britain," they said.
"Their decisions take into account a number of factors and ultimately these decisions are based on the panel’s expert judgment in selecting athletes who will be best placed to bring success for Team GB."