Gillingham was promoted to third in Atlanta when Andrei Korneev was stripped of his medal because of a positive drugs test, but the Russian was reinstated when it was ruled there was not sufficient evidence to establish the drug was covered by the Olympic Committees' medical code.
Gillingham, who would have become the first British swimmer to win a medal at three successive Games, was told at the time he would have the backing of the BOA in any appeal.
"I am bitterly disappointed at the decision," said Gillingham, who retired after the Games. "I believe there should be an appeal and I should have financial support to lodge an appeal. I have got to talk to a few people before deciding what to do next."
A BOA press officer, Pat Ewing, said they had taken the decision after discussions with their legal advisers. "We've told Nick that the decision is just not open to challenge from the BOA, the IOC or himself. We have every sympathy for his position."Reuse content