The advice came from Mark Stephens, a lawyer whose high- profile clients include Wikileaks founder Julian Assange who he has helped fight extradition proceedings brought by Sweden over allegations arising from encounters with two women.
Stephens called on the International Olympic Committee to come out publicly to support gay and lesbian athletes and to punish those countries where homosexuality is illegal.
Stephens said gay and lesbian athletes from such countries should apply for asylum in Britain when they arrive for the Games on grounds that they would be persecuted at home if they revealed their sexuality.
"I invite you to apply for asylum in this country on the grounds that you will face persecution at home if you are open about your sexual identity," Stephens said in a lecture just a few minutes from the Olympic arena in east London.
"The British government will have to hear your application and in doing so they will have to engage with the human rights abuses perpetrated against the lgbt (lesbian, gay, bisexual, and transgender) communities across the world," he said.
Same sex acts between consenting adults are illegal in 78 countries, or 40 per cent of United Nations member states, according to the International Lesbian, Gay, Bisexual, Trans, and Intersex Association (ILGA), a global federation of gay rights advocacy groups.
In five countries - Iran, Mauritania, Saudi Arabia, Sudan and Yemen - such acts are punishable by death, according to the group.
Stephens, who said he was heterosexual but flattered that people sometimes assumed he was gay because of his support of gay rights, said a mass asylum request during the Games would draw attention to the persecution of gays and lesbians.
"People talk about legacy in terms of the regeneration of a few acres of London, when in reality, the legacy should be a human legacy," he said.
In 2010, the UK supreme court ruled that gay and lesbian refugees at risk of persecution in their home country for their sexuality are entitled to asylum in Britain.