Carney, who has come under fire from supporters of Brexit for his stance in the EU referendum campaign, has said he will announce by the end of the year whether he will take up an option to stay at the BoE until 2021 rather than stick to his current departure date in mid-2018.

“The PM has been clear in her support for the governor, the work he is doing for the country,” her spokeswoman said.

“It is clearly a decision for him, but the PM would certainly be supportive of him going on beyond his five years … The PM has always had a good working relationship with the governor of the Bank of England and intends to continue that.”

Asked if Carney was the best man for the job, the spokeswoman said: “Absolutely.”

Carney’s plans have gripped financial markets after a weekend of conflicting media reports over his future, with his possible early departure cited as a risk to sterling, which has already been driven down by the perceived negative effects of Britain’s exit from the EU.