Labour MP Dame Margaret Hodge says "this debate will not go away" until the government has acted properly.
She says looking at the tax gap is not enough because it does not measure tax not paid by global digital companies.
She says ensuring fairness is "not about castigating the rich" but about funding the services the country needs, and allowing the 85% of people who pay their taxes automatically through PAYE to have faith in the system.
She says the "government won't be able to ignore the voice of Parliament" on this issue because "quite simply to do so would be morally wrong and totally unprincipled".
"We have become the jurisdiction of choice for too many kleptocrats," she says. "We will never build global Britain on the back of dirty money."
She asks the government to extend transparency to the UK's crown dependencies and overseas territories, and to support them in setting up public company registers.
She turns to the question of digital companies, saying we need "country by country reporting" of digital company's revenues and profits.