Polly Billington, MP for Thanet, said she was pleased that “more than 6,000 children” in her constituency would benefit from the change.
Education Secretary Bridget Phillipson told BBC Radio 4’s Today programme it was her “moral mission” to make sure fewer children grew up in the kind of poverty she experienced.
“We know if children are arriving at school ready to learn that makes a massive difference to their outcomes”, she said.
“If you’re hungry, it’s really hard to concentrate.”
But the Institute for Fiscal Studies think tank said that while the rule change would cut child poverty to a degree and would be cheaper than making free school meals universal, “other measures, such as lifting the two-child limit, would have a lower cost for each child lifted out of poverty”.
Labour is yet to decide whether to scrap the two-child benefit cap.
Speaking about the cap, Sir Stephen said: “We will have to wait for the child poverty task force to produce its strategy later on this year to see what extra levers they need to pull to help more children out of poverty.”