BBC Trust chair and HSBC non-executive director Rona Fairhead has been urged to step down from the Corporation over the bank's tax avoidance scandal by Chair of the Public Accounts Committee, Margaret Hodge.
Ms Hodge, who was speaking as executives from the bank appeared before MPs to face questions over claims that its Swiss private banking arm helped clients avoid millions of pounds in tax, grilled Ms Fairhead about her oversight of events.
Ms Hodge said Ms Fairhead should quit her BBC role or the Government should sack her, because she had been "either incredibly naive or totally incompetent".
Ms Hodge said: "I don't think that the record that you have shown of your performance here as the guardian of HSBC gives me the confidence that you should be the guardian of the BBC licence fee payers' money.
"You should think about resigning. If not, the Government should sack you."
But Ms Fairhead insisted she had been "unyielding" about any wrongdoing.
Ms Fairhead, who had served on the audit committee of the bank, said they were "horrified" to find out about the scandal but said she could only deal with evidence that had been presented.
She added: "I think that first and foremost the people who are most culpable are those people who evade taxes."
ITV News' economic editor Richard Edgar reports:
Ms Fairhead also denied reports that she is paid £10,000 a day by the bank.
HSBC's annual report showed she received £513,000 in fees and benefits last year including a £334,000 fee as non-executive chairman of HSBC North America Holdings.
In a statement the BBC Trust told ITV News: "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."
The same hearing also saw HSBC's chief executive Stuart Gulliver insist he was the right person to lead the bank after being quizzed over his own tax affairs.
He was questioned about claims that he funnelled £5m of his own money into a bank account set up by a company in Panama.
Mr Gulliver said he was now paid and taxed in the UK and the details of the payment came from 17 years ago when he was based in Hong Kong.
He said: "There was no tax evasion, no avoidance. It was simply done for privacy reasons. I have paid millions of pounds of tax at the top rate."