Mr Pennant-Rea said in his resignation letter to the Chancellor, Kenneth Clarke, that he was resigning "with great regret" to avoid the possibility of the Bank being damaged by "some foolish mistakes that I made, albeit more than a year ago".
Mr Pennant-Rea quit his £180,000-a-year post after details of his affair with the journalist Mary Ellen Synon were published in the Sunday Mirror.
The Governor of the Bank of England, Eddie George, said in a statement yesterday that Mr Pennant-Rea's resignation was a matter of "deep personal regret".
Ms Synon revealed in a classic kiss-and-tell report last Sunday how she and Mr Pennant-Rea, 47, had made love on the carpet of Mr George's dressing room at the Bank. Since the confessions, the City has been braced for his departure, with senior banking sources saying he had no alternative but to go.
The Prime Minister, John Major, was told about the resignation yesterday morning, but his office dismissed as "speculation" suggestions that Mr Pennant-Rea had been forced out over the Bank's mishandling of the Barings collapse.
In his resignation letter, Mr Pennant-Rea criticised newspaper coverage of the affair. "I thought that Britain would benefit from greater job mobility between the private and public sectors . . . But I do know that many good people in the commercial world are put off by the tabloid intrusion into the private lives of those in public positions."
Replying to the letter, Mr Clarke wrote: "I am very sorry indeed that you have decided to resign . . . You have done an exceptional job as Deputy Governor."
Ministers and Labour leaders reacted with surprise and outrage. Ministers privately said it was wrong for Mr Pennant-Rea to have resigned over his affair. "It's getting ridiculous. It seems there's a policy of one bonk and you are out," said one minister.
A senior government source said: "I am not aware of any [such] policy. Frankly, the Square Mile would be depopulated."
Mr Pennant-Rea was reported to have begun a relationship with Ms Synon, 44, four years ago. Ms Synon, speaking on Irish radio from a secret hiding place, was yesterday unrepentant.
"If you are going to dump," she said, "don't dump a financial journalist if you are the Deputy Governor of the Bank of England. If he had even been vaguely nice about this, I would probably have cooled off in 20 minutes. But the fact that he was . . . vicious about it just made me very angry. And nothing could be angrier than an Irish-American financial journalist who has been badly treated."
Mr Pennant-Rea's wife, Helen, backed his decision to resign, saying that he had paid "a high price" for staying with his family.
Reading from a statement on the doorstep of her home in Parsons Green, west London, she said: "I support and respect my husband's decision to resign from the Bank," she said. "His relationship with Ms Synon ended over a year ago and Rupert told me about it then. Over the last year we have endeavoured to rebuild our marriage . . . Rupert has paid a very high price for taking the right decision and staying with us . . ."
`Reliable' Rupert, page 3
Leading article, page 18
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City comment, page 33