Wanted: suitable candidate to run one of the world’s leading central banks. Applicants should demonstrate the economic acumen of a Keynes, the diplomatic skills of a Metternich, the political cunning of a Machiavelli, and the hide of a rhinoceros. Those interested should register their interest with the Right Hon Philip Hammond Esq at HM Treasury. Interviews will take place in the coming months and the name of the new governor will be announced in the autumn.

Now that there is a bit of Brexit breathing space, Hammond can get on with a couple of the other issues in his intray, one of which is to find a successor to Mark Carney at the Bank of England when he leaves next January.

Hammond has already twice persuaded Carney to stay on at Threadneedle Street from his original summer 2018 scheduled departure date but knows that there will be no further extension. As a result, the Treasury is starting to think about who might be a suitable replacement.

The chancellor warned while in Washington DC for the spring meeting of the International Monetary Fund that some potential candidates might be deterred from applying due to the toxic political atmosphere in the UK as a result of the Brexit process.

This seems unlikely. Running the Bank of England is a plum job and carries enormous prestige. Yes, Carney has taken a lot of stick from Tory MPs over Brexit but every central banker these days can expect a bit of political rough and tumble. Ask Jerome Powell of the US Federal Reserve, who is on the receiving end of incessant demands from Donald Trump to stimulate the American economy. Or Mario Draghi, of the European Central Bank, faced with the near-impossible task of keeping all 19 members of the single currency happy.

It was all a bit different when Carney’s predecessor, Mervyn King, became the Bank’s governor in 2003. Back then, growth was steady and inflation deviated only marginally from its 2% target. All Threadneedle Street’s monetary policy committee needed to do was give an occasional tweak to interest rates.

But the financial crisis and its aftermath changed all that. Anybody who thinks a central bank is above politics and can be run by a pure technocrat really hasn’t been paying attention. In the past decade, the Bank of England has expressed controversial views about reducing the UK’s budget deficit, Scottish independence and the likely effects of a no vote in the EU referendum. The fact that there has been no lasting recovery despite rock-bottom interest rates and oodles of quantitative easing means that central banks are under scrutiny as never before. Any candidate hoping for a quiet, cloistered life should not be applying and would not be worth interviewing if they did.

So who gets the gig? One school of thought is that Brexit makes it inevitable that Hammond will go for one of the home-grown candidates rather than someone for another country. A few eyebrows were raised when Carney was appointed in 2013, the argument being that Britain – a nation that specialises in financial services – should be capable of finding one out of 66 million people suitable to run the Bank of England.

If the government does go down that route, there are plenty of names to consider. Sir Jon Cunliffe has an impressive-looking CV, having worked at the Treasury and as the UK permanent representative in Brussels before becoming one of the Bank’s deputy governors. Cunliffe knows how EU works, which could prove useful whichever way the Brexit process pans out.

Andrew Bailey, the chief executive of the Financial Conduct Authority, is another considered a safe pair of hands, although perhaps a bit too safe. It is not that Bailey’s time running the watchdog has had its share of problems because that is always going to be the case with a body that is supposed to root out wrongdoing. Rather, the question is whether anyone actually fears the FCA. A Bank of England governor needs to be feared, as Carney certainly is.

Ben Broadbent, the Bank’s deputy governor for monetary policy and Andy Haldane, the Bank’s chief economist, are also mentioned among the list of runners and riders for the job. The question mark over Broadbent is whether he actually wants the job enough; Haldane would have a better chance if John McDonnell were chancellor.

Spreading the net wider, Hammond might want to talk to Shriti Vadera, who worked for Gordon Brown and is now the chair of Santander UK; and Minouche Shafik, a deputy governor of the Bank before becoming director of the London School of Economics.

All this, though, suggests that Hammond is set on giving the job to a Brit, and there is no evidence that this is the case. Hammond likes and admires Carney. He thinks people sit up and take notice when the governor holds forth at international meetings, and that he is good for the UK’s reputation. Every time Hammond goes to an IMF meeting, he sizes up possible candidates for the Bank job. He is, for example, a big fan of Agustín Carstens, the Mexican-born general manager of the Bank for International Settlements.

But the likeliest overseas candidate – and one who ticks an awful lot of boxes – would be Raghuram Rajan. He is a distinguished economist, has run the Indian central bank and so knows a think or two about how to handle political pressure, and is a good communicator; his appointment would suggest that Global Britain might be more than a slogan. Rajan says he is happy where he is at Chicago Booth school of Business and may play hard to get. But, then again, so did Carney.