Jones, who was also previously chief secretary to the Treasury, wrote on X, external that the Digital ID programme was unfunded.
While praising the VAT cut as “good”, he said “the government will have to set out how it will pay for its new policies at the budget”.
Conservative Shadow Chancellor Mel Stride also criticised the use of the Digital ID budget to fund the VAT cut.
“The cuts to the Digital ID card budget are not real because the money was never provided in the first place.
“We are only one day in and already its smoke and mirrors on the public finances.”
Business Secretary Jonathan Reynolds told the BBC’s Today programme a VAT cut to electricity bills would be funded through a “straightforward switch spend” redirecting money for digital ID.
He said money for digital ID “would have had to have been found” and that scrapping the scheme removed “pressure” from the budget allowing the government to “give real help to people”.
But the Office for Budget Responsibility said last November that digital ID would have to paid for out of savings from government departments and these had not yet been identified.
The spending watchdog said bringing in Digital ID had “provisionally forecast to cost £1.8bn in total over the next three years”.
Government sources have insisted that departments have been working to find savings to fund Digital ID since the OBR made its forecast in November and this money would now be reallocated to fund the VAT cut.
Household energy prices rose by 13% for millions of people in England, Scotland and Wales at the start of July, under regulator Ofgem’s price cap.
Price rises were driven by the higher cost of gas, but have a relatively limited impact owing to warm weather and lower energy use during the summer months.
However, higher energy prices caused by the US-Israeli war with Iran, which has constrained global supplies of oil and liquified natural gas, are likely to persist into the winter, according to analysts.
The VAT cut only applies to the current financial year — any decision to keep it in future years would have to be made in a Budget.
The government expects it will lower inflation by 0.1 percentage points.
In his first speech as the UK’s prime minister, Burnham vowed to provide “breathing space” for households struggling with the cost of living.
On Tuesday, he said the VAT cut would “put more money in people’s pockets”.
The VAT cut is the second intervention on energy bills by the government in six months.
Former chancellor Rachel Reeves removed one levy and shifted others onto general taxation to lower bills in April.
Burnham’s new cabinet is due to meet for the first time at lunchtime on Tuesday.
The End Fuel Poverty Coalition welcomed the reduction, but said it “does not address the scale of what households are facing”.
Simon Francis, the group’s co-ordinator, said Burnham’s government must “go even further” with targeted support for those most in need.
He added: “This breathing space is also not a cure. The only way to bring bills down for good is to change how they are set.”
