The head of the BBC Trust has been told by a senior MP she is "totally incompetent" and should resign.
Margaret Hodge, chair of the Commons Public Accounts Committee, gave Rona Fairhead a dressing down during a hearing over failings at HSBC bank where she had oversight of the bank's audit committee.
It followed revelations the bank had allowed tax avoidance and evasion to go on while she was in that role at the bank, and which she only moved from in 2010.
Ms Hodge said: "I'm going to say something as a licence fee payer.
"I think you knew (there was) tax evasion, or you didn't know and I think in that case you are either incredibly naive or totally incompetent and I don't think that the record that you've shown, or your performance here as a guardian of HSBC, gives me the confidence that you should be the guardian of the BBC licence fee payers.
"I really do think you should consider your position and you should think about resigning and if not, I think the Government should sack you."
Ms Fairhead said she totally refuted the accusation.
She said: "In the period when I was chair of the committees I was in a non-executive position of oversight … at that time I think it is reasonable for a non executive director to rely on the policies, the management structures in place, to rely on independent experts that had been commissioned because of their expertise to highlight issues.
"That was absolutely what we insisted on. You can ask anybody in the bank, we were unyielding if we discovered or thought or suspected of any wrongdoing. So I absolutely refute what you said."
Ms Fairhead had been grilled by the committee for nearly two hours over her role at the bank during the period when the alleged tax evasion went on.
She was repeatedly asked how it was her committee had not picked up the tax evasion, when its role was to make sure the bank was adhering to the rules and regulations of the banking industry.
She revealed that she is paid £334,000 a year by HSBC for between 75 and 100 days of work a year, carries out around 150 to 180 days of work a year for the BBC Trust and around 25 days work a year for Pepsi.
Also facing questions were current HSBC CEO Stuart Gulliver and former CEO Chris Meares who were both attacked over their roles.
Last month, a number of stolen files were made public in a French newspaper which claimed that HSBC's Swiss private banking arm helped clients in more than 200 countries evade taxes on accounts containing £77bn ($119bn).
The alleged evasion was said to have taken place at HSBC's private bank in Switzerland in the mid-2000s.
HSBC chairman Douglas Flint previously told Parliament's Treasury Select Committee that the executives at the time bear "fairly direct responsibility for what went on in the private bank during their stewardship".
Mr Meares told the Public Accounts Committee: "I was not personally accountable for the actions of individuals in Switzerland but I absolutely share responsibility for the events, if any of these reported practices went on, for what happened on my watch."
When Ms Hodge asked Rona Fairhead if she knew what was going on, the BBC Trust chairwoman said: "No I did not.
"Was any evidence brought to the committee of the practices that we are talking about now, the answer is absolutely no."
The BBC Trust has defended Ms Fairhead, saying in a statement: "Rona Fairhead is committed to her role as Chairman of the BBC Trust, representing the interests of licence fee payers. As she has said before, the BBC is her main priority."