Large private companies face having to disclose how much tax they pay after the Senate overturned a controversial shield law passed by the Turnbull government less than a month ago.

In a stunning change of heart, crossbenchers Nick Xenophon and Ricky Muir reversed their previous position in support of an exemption for privately owned companies with revenues of more than $100 million a year.

The Greens, supported by Labor, led the push to reverse the exemption in response to a Fairfax Media investigation, published Monday, which revealed one of the key stakeholder organisations used to justify exempting the largest private companies was actually a front group without any members.

The Family Office Institute Australia, which was quoted at length in a Senate committee report, was established in August by two lawyers and a Canberra lobbyist who represent Australia's ultra-rich in disputes with the Australian Tax Office.

Greens Senator Peter Whish-Wilson said the "Better Targeting the Income Tax Transparency Laws" Act needed to be repealed because the Senate had been "astroturfed" and "conned" by the Family Office Institute.

The concept of astroturfing, which is much more prevalent in US politics, involves the use of "artificial grassroots" to push a narrow political agenda on behalf of powerful interests.

During debate, Senator Whish-Wilson said the Family Office Institute was a "particularly acute" example of those with resources being able to deploy lobbyists to get a legislative result.

He said the matter was of significant public interest and the Greens acted once "new information came to light".

"And that information was basically that we've been 'astroturfed' by a front organisation that appeared during the committee process and senators themselves have admitted had an impact on their decision," he said.

"I don't think there is a single Australian out there, besides perhaps ones worth more than $100 million, who would oppose this legislation."

The amendments passed were attached to the government's multinational tax avoidance bill – Joe Hockey's last act as Treasurer.

The government will now have to decide whether to pass the bill through the House of Representatives or reject the amendments and send the bill back to the Senate with changes.

The Minister for Small Business and Assistant Treasurer, Kelly O'Dwyer said: "The Australian Taxation Office has the power to look at all of the financial and tax arrangements of Australian-owned private companies.

"These amendments will do nothing to increase the ATO's powers.

"Labor and the Greens are clearly playing politics.

"The delay of the multinational tax bill will stop increased penalties for multinationals who flout the law and don't pay their fair share of tax."

Labor senator Sam Dastyari said Prime Minister Malcolm Turnbull and Treasurer Scott Morrison would be out of step with society if they keep up the fight for large private companies to remain cloaked in tax secrecy while conducting a conversation on raising the GST on ordinary Australians.

Tax transparency campaigners, who worked for years to convince the former Labor government to pass the law to demand companies publish their annual tax contribution, welcomed the news.

"It's a great day for democracy when a sneaky attempt to ensure more secrecy around corporate tax is thrown out," said Mark Zirnsak, spokesman for the Tax Justice Network, an established group with dozens of member organisations, including charities, churches and unions.

The Greens amendment was supported Senators Xenophon and Muir after the insertion of two key clauses. The first would allow companies in critical commercial negotiations with dominant players – for example, Coles and Woolworths – to appeal to the Tax Commissioner for an exemption on disclosure.

And the public list of tax paid, which will be maintained by the Australian Tax Office, will include a disclaimer that the information does not necessarily provide the "full picture" of a company's tax affairs.

Senator Xenophon said he had been persuaded by "arguments I thought had some credibility at the time".

But he since learnt that all the information to be provided on the register can be obtained in a $38 company search through the Australian Securities and Investment Commission.

The Coalition voted against the amendment.

Richard Gilbert, the director of the Family Office Institute, said: "We are very disappointed with this outcome, which sends the wrong signal to free enterprise in Australia. It's clearly discriminating against one class of taxpayer over another."

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