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.

A fire, started by a spilled oil lamp, swept through Exhall pit near Bedworth on 21 September, 1915, threatening the lives of the 375 men working there.
The majority of the men were led to safety through a ventilation shaft by the man in charge underground.
A circle of 14 trees, one for each man who died, has been planted around a granite memorial.
The memorial, in St. Giles Meadow, was unveiled by the High Sherriff of Warwickshire.

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But this 7ft tall New Zealander with a sleeve of tattoos is fast becoming the star of the NBA play-offs and is even putting the league's most valuable player Stephen Curry in the shade.
Adams and his Oklahoma City Thunder side beat Golden State Warriors 118-94 in game four of the Western Conference finals on Tuesday, to lead last year's champions 3-1 in the best-of-seven series.
It was the first back-to back defeats for the Warriors this season, a team who set a new NBA record of 73 wins in the regular season.
Russell Westbrook and Kevin Durant were the stars of the show for the Thunder, but even they were eclipsed by a moment of magic from Adams.
The 22-year-old, who scored 11 points and seven rebounds in the win, threw a one-handed bullet pass to Andre Roberson just before half-time.
More than 22,000 tweets were sent in an hour about Adams' baseball style throw and the player began trending on Twitter in his native New Zealand and the US.
Then there was a young fan who turned up to the game at Oklahoma's Chesapeake Arena, dressed as Adams with a fake moustache and tattoos in tribute to her hero.
Many Twitter users felt the youngster was the real star of game four and even Adams himself tweeted that it was "absolutely amazing".
In game three Adams hit the headlines after Warriors forward Draymond Green kicked him in the groin area, but avoided suspension.
It led to Thunder fans using the hashtag #standupforsteven in the build-up to Tuesday's game.
Adams has rarely been out of the headlines in the series. After game one he had to apologise for referring to the Warriors' players as "quick little monkeys".
"It was just a poor choice of words," said Adams, who blamed differences in dialect for his comments.
"I wasn't thinking straight. I didn't know it was going to upset anyone."
Then there is his family - Adams is the youngest of 18 siblings.
His brothers are around 6ft 10in to 6ft 11in, while his sisters stand at 6ft 5in to 6ft 6in.
Six of his brothers have played basketball for New Zealand, while his half-sister Valerie, 31, is a double Olympic champion shot putter.
The former president of the Maldives, Mohamed Nasheed, has been granted refugee status in the UK, according to his lawyer.
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A memorial has been dedicated to 14 men who died in a Warwickshire mining disaster a century ago.
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With his long, ragged hair and handlebar moustache, Steven Adams looks like he has stepped out of the 1970s.