They accuse him of instigating the deadly inter-ethnic violence that broke out last week and he also faces criminal charges related to his former position as head of the agency that controls state assets and loans.
Bakiyev arrived in Britain on June 13, weeks after his father, former president Kurmanbek Bakiyev, was ousted in violent protests in April.
"Mr. Bakyiev was screened in accordance with normal procedures for port of entry asylum claims, and then granted temporary admission pending the consideration of his claim," a statement from Carter-Ruck Solicitors said.
In comments released by the law firm, Bakiyev rejected the charges against him, saying they were "bogus".
"I have been forced into exile in fear for my life. The interim government in Kyrgyzstan accuses me of new crimes every day," he said.