Raghuram Rajan is the only outsider among the top contenders for the Bank of England top job

Raghuram Rajan has delivered some uncomfortable economic truths in a career spanning the International Monetary Fund and powerful positions in India. The question is whether Brexit Britain is ready to hear them from another foreign Bank of England governor.

The job of stewarding the U.K.'s monetary policy and maintaining its financial stability has rarely been more political, and Rajan is the only outsider among the top contenders in the running to replace Mark Carney, according to bookmakers and economists who follow the 325-year-old institution.

Carney's tenure has been overshadowed by the convulsions over Brexit, with some hard liners in the governing Conservatives accusing the Canadian of exaggerating the economic pain and underplaying the benefits of leaving the European Union. As the party chooses a new leader following the resignation of Prime Minister Theresa May, her potential successors have vowed to deliver Brexit, and the latest deadline is Oct. 31.

Rajan has made sympathetic noises toward the U.K.'s dilemma, particularly the disillusionment in parts of the country that fueled the Brexit vote. He told the Times newspaper in March, though, that success depends on the U.K. reengaging with the world.

That would start with his appointment, according to David Blanchflower, an economics professor at Dartmouth College and a former Bank of England policy maker. The other top candidates for the job, including front-runner Andrew Bailey, already work at the bank or financial regulator.

"It's a pretty unimpressive bunch, with Rajan sitting head and shoulders above the rest of them," Blanchflower said. "The problem is, why would anybody want to put themselves in the position of having to deal with Brexit?"

Rajan, 56, a professor at the Chicago Booth School of Business, declined to comment about his potential candidacy when contacted by Bloomberg, as did the Bank of England.

The U.K. Treasury, which is responsible for hiring the next governor, declined to comment on who had applied by last week's deadline. Chancellor of the Exchequer Philip Hammond has stressed the need to look internationally for the next appointment, though it's not clear if he will still be in his job when the decision is made.

What is clear, though, is that Rajan has the right sort of track record. He was chief economist of the IMF from 2003 to 2006, and then worked as an adviser to the Indian government before becoming governor of the Reserve Bank of India in 2013.

At the elite Jackson Hole annual economic gathering in 2005 when he was at the IMF, Rajan warned that risks were building up in the global financial system. At the time, former U.S. Treasury secretary Larry Summers criticized Rajan as a "luddite." Three years later, Lehman Brothers collapsed.

As RBI governor, Rajan introduced inflation targeting and led an effort to clean up bad loans in the banking industry. He remained for just one three-year term running India's central bank after heavy criticism from segments of the government for offering opinions on matters unrelated to monetary policy.

Subramanian Swamy, an outspoken lawmaker in Prime Minister Narendra Modi's ruling party, said Rajan was "mentally not fully Indian" and kept interest rates too high. In 2016, Swamy wrote a letter to Modi calling for Rajan to be either fired or dismissed at the end of his term.

In his 2017 book "I do what I do," Rajan said he warned the government against demonetization - an attempt to withdraw cash from circulation - saying the short-term economic costs would outweigh the long-term benefits.

"He handled some very treacherous shoals very well," said Anne Krueger, a former IMF first deputy managing director who helped recruit Rajan. "He did not cave under political pressure and on the other hand he did the best he could to advance what he thought was right."

Political attacks have also been a hallmark of Carney's time at the Bank of England. Pro-Brexit Lawmaker Jacob Rees-Mogg at one point called him a "second-tier Canadian politician" who failed to get a job at home as well as an "enemy of Brexit."

Rajan has indeed hinted the role could be too politically fraught. Central banking jobs are "very polluted," he said in an interview with Forbes published last week. "You have to have a very good sense of where the political terrain lies and how far you can go without upsetting the balance."

In his latest book published this year, "The Third Pillar: How Markets and the State Leave the Community Behind," he argues that neglect of parts of society led to a rise in populism and mistrust. Bank of England Chief Economist Andy Haldane, who is also in the running to succeed Carney, has cited the book in his last three public appearances.

Those political antennae will be vital to navigate Brexit, according to Arvind Mayaram, who was the top bureaucrat in the Indian Finance Ministry while Rajan was central bank governor.

"The volatility and uncertainty that comes with it will require a very steady hand," said Mayaram. "He can hold his own and speak his mind. He would not let go of those core principles, which would be necessary for the central bank to steer a course in very turbulent waters."