The Foreign Secretary told a meeting of business leaders in Singapore that Europe's recent decision to deny visas to senior Burmese officials made their inclusion at the Asia-Europe Meeting (Asem) in London in April "impossible".
Asem is a forum linking the 15 members of the European Union with Japan, China, South Korea and some members of the Association of South-East Asian Nations (Asean).
Asean admitted Burma to its ranks this year, despite heavy Western criticism of Rangoon's record on human rights and its flourishing drugs trade.
"There is a common European position across all European countries not to grant visas to ministers from Burma, which will make it impossible for us to consider the inclusion of Burma in the Asean process next year," Mr Cook said at the end of a four-nation tour of South-East Asia.
"Burma is the largest single world producer of opium, and it has achieved that infamous position precisely because it is a government that does not act against the drug barons," he said.
He added: "It is not only a deeply repressive regime, but it is also a deeply irresponsible regime in that it is one of the few governments in the world whose members are prepared to profit out of the drugs trade rather than to seek to suppress the drugs trade."
Mr Cook told a news conference before leaving for home that Britain could bar Burma from the summit because Asem was not a bloc-to-bloc meeting but a voluntary dialogue between nations.
He said he had found "deep common recognition" of the problem of Burma in the Asian capitals he had visited "both in terms of its government system and in terms of the connivance of the government in the drugs trade".
But he said there was "an honest difference of approach" as to how to resolve the issue and persuade Rangoon's State Law and Order Restoration Council (Slorc) to change.
"In Europe, we have taken the view that we cannot have dialogue with a government that is both as repressive as Slorc and as irresponsible in its connivance with the drug barons," he said.
"In South-East Asia there is, particularly in Asean, a belief that the best way forward is for dialogue with Slorc. What I have found encouraging is that there is in every capital I have been to a recognition that there is a serious problem here that must be addressed."