With the Democratic Unionist Party likely to oppose the Government on such a vote, it left her facing a possible embarrassing defeat, the Opposition claimed.
An amendment was expected because – like the notorious £350m-a-week extra for the NHS – zero-rating of fuel was a key plank of the Vote Leave campaign that secured Brexit.
Another likely challenge was over the issue of “period poverty”, with ministers under pressure to agree to put in free sanitary products in schools.
The controversy comes hard-on-the-heels of the row over the Conservatives seizing control of all Commons committees – despite losing their majority at the general election.
The Independent revealed that plan ahead of it being forced through in September, potentially helping ministers to ram through up to 1,000 “corrections” to EU law ahead of Brexit.
Now Labour has accused the Government of a similar manoeuvre to prevent most amendments to the Finance Bill, which will enact last week’s Budget.
“Once again we have further evidence of the Government’s unprecedented rigging of Parliament because they cannot rely on their backbenchers or the DUP,” said Peter Dowd, the Shadow Treasury Chief Secretary.
“This comes in the wake of the Tories stitch up of standing committees and its undemocratic and arrogant decision to ignore opposition motions.”
And Paula Sherriff, the Labour MP who successfully amended the Budget over the so-called “tampon tax”, told The Independent: “That ended up being welcomed on all sides of the House.
“And, this year, there are MPs across parties who want to press for action on period poverty and get a clear timetable for the tampon tax to come to an end with commitments to continue support for women’s services.
“We can’t let the Government shut down the debate. If they think this is over, they should think again.”
However, the Government dismissed the controversy, describing the change to procedures for amendments as “a practical modernisation”.
In March last year, George Osborne was forced to announce the abolition of the 5 per cent VAT charged on women’s sanitary products, after a cross-party revolt.
Labour campaigners joined forces with Eurosceptic Tories keen to assert Britain’s power to set its own tax rates, forcing the then-Chancellor into the climbdown.
A similar alliance also forced Mr Osborne to scrap a proposed VAT hike on solar panels, wind turbines, hydropower equipment and energy efficiency products, from 5 per cent to 20 per cent.
But, crucially, both rebellions were only possible because the Government tabled an “amendment to the law resolution” – allowing amendments outside the narrow scope of measures in the Budget itself.
Following last Wednesday’s Budget, that amendment was not put forward as normal, preventing revolts on wider issues not “in the founding resolutions” of the Budget.
Labour said this had happened only five times since 1929 – but each time had been immediately before, or after, a general election, when a Budget needed to be rushed through.
In contrast, the current Finance Bill is the second of this Parliament, because one was passed immediately after the snap June election.
“This is a Government desperately clinging to power and hiding from scrutiny,” Mr Dowd added.
In February, pro-EU MPs attempted to embarrass Brexit campaigners with an amendment attempting to pave the way for the extra £350m-a-week for the NHS they had promised.
However, Brexit-backing MPs refused to vote for the attempted change to the EU Withdrawal Bill. Last week, the Chancellor pledged £350m to the NHS – but to last the entire winter, not every week.
In the same way, an amendment was expected to the Budget Bill to highlight a second high-profile Vote Leave pledge, over VAT on fuel.
During the referendum campaign, the group claimed that quitting the EU would save British households £1.7bn a year on heating and lighting, or £64 a year per household.
The government would be free to scrap VAT on domestic fuel, Boris Johnson, Michael Gove and the Labour MP Gisela Stuart said – meaning “fuel bills will be lower for everyone”.
VAT on domestic fuel, introduced in 1993, is set at 5 per cent and cannot be reduced under EU rules, they argued.
They also claimed the tax hits the poorest hardest, because they spend three times more of their income on household energy than rich households.
But a Treasury spokesperson said: “This is a practical modernisation of the resolutions. It will make no difference to what we expect will be a broad and wide-ranging debate on the Budget and state of the economy over the next few days.”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies