The committee was reacting to her admission that she had failed to inform the bank, when she joined as chief operating officer in 2013, that her brother, Quintin, worked in a senior strategy role at Barclays.
The failure came to light after she filled in a questionnaire for the committee as it scrutinised her promotion to deputy governor - a job that would give her oversight of bank regulation.
Following checks, she admitted the omission breached the Bank's guidelines - which she had helped draw up - covering potential conflicts of interest.
She was handed a warning by the Bank after the blunder was discovered. She apologised for what, she insisted, was an "honest mistake".
In its assessment of her actions on Tuesday, the committee stopped short of recommending she be fired.
But in her resignation letter to Bank governor Mark Carney and chairman of the Bank's Court, published by the Bank, it was confirmed she had already volunteered to go but that request had been turned down.
She wrote: "Last week I offered you my resignation in recognition of the fact that I made a mistake in not declaring my brother's work on the forms that the Bank requires. It has become clear to me that I should now insist.
"As I have said, I am very sorry for that mistake. It was an honest mistake: I have made no secret of my brother's job - indeed it was I who informed the Treasury Select Committee of it, before my hearing.
"But I fully accept it was a mistake, made worse by the fact that my involvement in drafting the policy made it incumbent on me to get all my own declarations absolutely right.
I would like to repeat my apologies for that, and to make clear that the responsibility for all those errors is mine alone."
Mr Carney said in response: "While I fully respect her decision taken in accordance with her view of what was the best for this institution, I deeply regret that Charlotte Hogg has chosen to resign from the Bank of England."
He went on to praise her role in overhauling the Bank's management and operations, saying she had "inspired countless colleagues at the Bank and attracted a new cohort of professionals to it".
The Bank said it was to undertake a review of its compliance procedures and had already implemented some measures to better safeguard governance of its code of conduct.
The committee's chair, Andrew Tyrie MP, said: "This is a regrettable business with no winners.
"Ms Hogg has acted in the best interest of the institution for which she has been working. This is welcome.
"It is also welcome that the Bank has responded immediately by announcing an internal review. The Bank's governance is already in much better shape than it was a few years ago.
"It is something to which the Governor and Court has been committed for some time. But there is clearly more to do."
SKY News.
