World number one and two-time European champion Aaron Cook wrote to Hugh Robertson in a bid to state his case after he was controversially overlooked in preference to Lutalo Muhammad.
Cook - whose record is far superior to Muhammad - claims he is being punished for his decision to train alone, outside the official team set-up.
British Taekwondo have now nominated Muhammad after three separate selection meetings and the British Olympic Association are still refusing to rubber-stamp his place, with the World Taekwondo Federation now claiming they will launch an immediate investigation.
"If I were to step into this process I would set a very dangerous precedent because at that point everyone else who has a similar gripe, and I am expecting a record number of these, will automatically come straight to me," Robertson told reporters at a lunch organised by the Sports Journalists' Association.
"Is it embarrassing for us? The honest answer is yes because you would rather not see our sports getting criticised by their international federations. That said it is probably inevitable before a home Olympics.
"On the few occasions that politicians have tried to influence the selection of a team then disaster follows.
"I thought one of the sublime ironies of the London 2012 process was that the two most high-profile athletes that the Thatcher government tried to stop going to the Moscow Olympics are now the chairman of the organising committee (Seb Coe) and the chairman of the national Olympic committee (Colin Moynihan).
"That tells you that government interference in this area does not work.
"However, if this one ran on for a long time then clearly I will talk to the British Olympic Association about it, I speak to them regularly anyway."
Team GB officials are currently discussing the issue with the world governing body and it will be a pressing agenda point for a meeting of their board.
It means British Taekwondo's management is being caught in a biting pincer movement, with increasing criticism of their selection procedures.
"We are extremely disappointed by the way in which British Taekwondo’s selection process has been conducted and it is clear that the lack of a conclusive rationale has caused confusion," said World Taekwondo Federation secretary-general Jean-Marie Ayer.
"The manner of the selection is bringing our sport into disrepute among the UK media and major Olympic stakeholders due to a perceived lack of transparency.
"Our main concern is always that every athlete is given fair and equal consideration – their welfare must come first.
"We at the WTF have done our utmost to bring fair practices and transparency to our sport, and that is why we have committed to undertaking this review.
"People all over the world practise taekwondo because it represents sport in its purest form: an individual display of skill, speed and strength.
"It is essential that the WTF preserves that purity for its 201 member countries and 70 million practitioners with transparent and decisive governance.”