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He is also facing criticism for his supposed refusal to take orders from Britain's political classes, as well as his alleged anti-Brexit stance.
In two separate columns in prominent publications over the last two days, Carney has been on the end of a stream of anti-Bank of England rhetoric, with a Spectator column even calling for his resignation or sacking as a result of failings in his policy of forward guidance.
Writing in the second installment of his newly minted column in The Times, failed Tory leadership contender Michael Gove compares Carney to "the Ming Emperor, Lord of Ten Thousand Years, who employed the Mandate of Heaven to decide the fate of millions."
Gove's argument is that Carney's assertion last Friday that the Bank of England is "not going to take instruction on our policies from the political side," is some sort of affront to Prime Minister Theresa May, and that Carney is acting like a demagogue by refusing to yield to the prime minister's criticisms of ultra-low interest rates.
As Gove puts it in his column, titled "Experts' like Carney must curb their arrogance:"
"For the governor, this was an act of lèse-majesté and dangerous heresy. The prime minister was no more entitled to talk about the economy than I would be to undertake brain surgery."
There is one big problem with Gove's argument. Carney is perfectly within his rights not to "take instruction" from Theresa May or anyone in
Since 1997 - as has been frequently been pointed out in the last week - the bank has had total independence of setting monetary policy. The government sets its mandate, namely price stability and trying to keep inflation at around 2%, but has no say in how this is achieved.
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Granted there is a small caveat in the bank's mandate allowing the government to force its hand "in extreme circumstances," and when "the national interest demands it," but to do so would be without precedent, and highly unusual.
Elsewhere, in The Spectator, writer James Bartholomew criticised Carney's policy of forward guidance - the process of essentially giving verbal assurances about future monetary policy in order to influence the financial decisions of households, businesses and investors, and allow them to prepare for the future - calling it "reliably wrong."
When he first became governor in 2013, brought in by then Chancellor George Osborne, Carney committed to a standard eight-year term, but said that he would likely leave the post after just five years. He is expected to announce by the end of the year if he will stay until 2021, with the consensus currently that he will stay at the Old Lady of Threadneedle Street for his full time.
Bartholomew argues that Carney should "not be allowed" to complete his full term as governor, and that he should "shut the piano and go home."
As well as being criticised for not taking orders from politicians, and for forward guidance, Carney's allegedly anti-Brexit stance has also drawn the ire of pro-Leavers, Bartholomew among them.
"Mr Carney warned the nation in May that a vote for Brexit could lead to a recession - two consecutive quarters of negative growth. He appeared to be going beyond any formal Bank of England forecast. Effectively he was supporting the Remain campaign by backing Project Fear. He gave up the political neutrality expected of governors," he wrote on Thursday.
That is a view that was echoed in the run up to the referendum by Tory MP Jacob Rees-Mogg. In a hearing of the Treasury Select Committee (TSC) in March, Rees-Mogg accused the governor of making "speculative pro-EU comments" that are "beneath the dignity of the BoE."
Earlier in the week Chancellor Philip Hammond moved to try and stop any speculation about any change in the bank's role, or about Carney's job, saying: "There will be no change in monetary policy … Monetary policy is independently determined, that will continue to be the case," in a hearing of the TSC.
For the time being, the government remains supportive of the BoE, as it should - but there is a growing divide between the bank and many supporters of Brexit, and that could be damaging.