Nasheed, the opposition leader, was controversially jailed for 13 years under anti-terror laws last year.
He was allowed to travel to the UK to receive treatment on his spine.
His lawyer Hasan Latheef said Nasheed had been granted political refugee status, but the British government has not commented.
A former human rights campaigner, Nasheed became the nation's first democratically elected leader in 2008, ending three decades of rule by former strongman Maumoon Abdul Gayoom.
Why did the Maldives release its most famous prisoner?
In 2012, he was detained after being accused of ordering the arrest of a judge. He resigned months later amid an army mutiny and public protests over the judge's fate.
Nasheed alleged that he had been removed by a coup, but this was denied by his vice-president, who replaced him.
The current President, Abdulla Yameen, was elected in controversial polls in 2013 and is the half-brother of Mr Gayoom.
"Given the slide towards authoritarianism in the Maldives, myself and other opposition politicians feel we have no choice but to work in exile - for now," said a statement issued by Nasheed's office on Monday.
The Maldives foreign ministry said it feared Nasheed had used the request for medical treatment as a way to get out of his prison term.
It said the government was awaiting confirmation asylum had been granted. If confirmed, the Maldives government "would be disappointed the UK government is allowing itself to be part of this charade, and further, is enabling an individual to circumvent his obligations under the law", the statement said.
The former president of the Maldives, Mohamed Nasheed, has been granted refugee status in the UK, according to his lawyer.