This equates to one in five families, many of them low-income working families, which are struggling to provide their children with the basics.
The claims are made in a new analysis from the End Child Poverty coalition – Short Changed: The true cost of cuts to children's benefits.
The paper has looked into the effect of the policy decision not to increase Child Benefit and Child Tax Credit in line with the cost of living over the past three years.
In 2010, the government decided to freeze Child Benefit for three years and to link Child Tax Credit to the Consumer Prices Index (CPI) rather than the higher Retail Prices Index (RPI).
Then in 2012, the government said that most children's benefits and tax credits would be increased by just one per cent a year from 2013/14 to 2015/16 regardless of inflation rates.
The End Child Poverty paper finds that 4.1 million families and 7.7 million children have been affected by the below inflation rises of Child Benefit and Child Tax Credit over the past three years.
Of these, 1.5 million families with 2.5 million children say they have cut back on food as a result. A similar proportion say they have cut back on heating.
Nearly two-thirds of the families affect are low-income working families, who are living in poverty because of low pay. In fact, only one in five of the families have household incomes of more than £20,000 a year.
The End Child Poverty coalition wants to see a "triple lock" protection introduced for Child Benefit and Child Tax Credit which would make sure that they either rise in line with prices, earnings, or by 2.5 per cent – whichever is the highest. A similar system has already been announced by the government for the basic state pension.
End Child Poverty claims that under a "triple lock", 310,000 fewer children will be living in absolute poverty by 2020 than under the government's current policy.
Currently, there are 3.7 million children living in poverty, according to the government's latest statistics. Furthermore, six in 10 children living in poverty are in low-income working families. It has also been estimated, by the Institute for Fiscal Studies, that by 2020 as many as 750,000 more children could be living in poverty than today.
David Holmes, chair of End Child Poverty, said: "It is deeply worrying that parents are having to cut back on food, heating and other essentials that their children need in order to develop and thrive.
"The new government needs to seize the opportunity in the Queen's Speech to stop the rise in child poverty. During the election campaign David Cameron promised not to cut Child Benefit, now is the time for him to keep that pledge.
"We think it is vital that child benefits keep pace with the cost of living and that the government gives them the same protection as the state pension. This is an opportunity to be bold and to invest in our children's future."
The End Child Poverty coalition is made up of more than 150 organisations from civic society including children's charities, child welfare organisations, social justice groups, faith groups, trade unions and others.
The paper can be downloaded via http://bit.ly/1Jj1ah8