Millions of Americans face losing access to food assistance under proposed rule changes by the Trump administration, a new analysis has found.

The changes, if they had been instituted last year, would have resulted in 3.7 million fewer people and 2.1m fewer households receiving the Supplemental Nutrition Assistance Program, known as Snap or food stamps, during an average month, according to the study.

The altered rules would also reduce benefits received by many people, with 2.2m households set to have their average monthly assistance cut by $127. Nearly one million students would lose access to free or discounted lunches.

The analysis, by the not-for-profit Urban Institute, said that three planned changes to Snap would “significantly alter” food-based help provided to poor Americans, with disparities across the country in terms of impact. Benefits would be cut in most states, although states including Vermont, New York, Nevada and Connecticut would fare particularly badly.

The Urban Institute said Snap had a “proven track record of reducing both poverty and food insecurity”.

The US Department of Agriculture, which oversees the Snap program, has put forward new rules that would create stricter work requirements to be eligible for Snap and cap deductions for utility allowances. The third change would restrict the way 40 states automatically provide Snap to families once they get other types of federal assistance.

Sonny Perdue, the US agriculture secretary, wrote in a USA Today op-ed that the Trump administration was “taking steps to restore integrity to Snap and move people toward self-sufficiency”.

The rule changes, Perdue wrote, restore “the dignity of work to a sizable segment of our population, while it is also respectful of the taxpayers who fund the program”.