Margaret Hodge, chair of the public accounts committee, said major corporations should be stripped of their right to full privacy over their tax affairs.
She told the Independent new rules should be brought in forcing companies to make a full disclosure to MPs in closed sessions, which would allow their arrangements to be scrutinised.
Mrs Hodge told the newspaper: "We could have a committee of MPs overseeing them in private, the same way that the Intelligence and Security Committee operates. That has operated very effectively. There has never been a leak."
More top news
An Egyptian billionaire has offered to buy an island from Greece or Italy and develop it to host migrants fleeing war-torn areas.
The number of children having private tutoring has increased by more than a third in the last decade, according to a charity.
Girls should swap dolls for toys such as Lego and Meccano to get them more interested in science and engineering, top scientist claims.