This figure would double the 2.3 million children currently classed as living in poverty, under the official measure of having a household income less than 60% the median average.
Some 2.3 million children in the UK are living "materially deprived" lives but are not included in official Government statistics on poverty, according to a report.
The report from think tank Policy Exchange says that the existing financial threshold fails to take into account the impact on a child's life of issues like quality of housing, educational standards and whether he or she has been in the care system.
Work and Pensions Secretary Iain Duncan Smith is already consulting on a new measure of child poverty, to end the exclusive focus on income levels and reflect other aspects of what it means to grow up experiencing deep disadvantage.
Policy Exchange head of economics and social policy Matthew Oakley said the new measure should include factors including whether children are themselves parents; whether they live in temporary or poor-quality accommodation; if the family has unsustainable debts; and if the child has been taken into care, has criminal convictions or low educational attainment.
The report recommended the introduction of a new Child Poverty Bill to replace the Child Poverty Act 2010, which commits the Government to ending child poverty. The new bill would measure social poverty as well as household income.
"The current measure of child poverty needs changing," said Mr Oakley. "Simply assessing whether a child is in poverty on the basis of household income fails to take into consideration a number of serious issues. It leads us to think we are improving outcomes for children when in fact they can still be living severely deprived lives.
"A new measure, focused on income as well as factors such as the quality of housing and level of education, would likely increase the number of children in poverty. However, it would allow the Government to focus policy solutions on improving outcomes both now and in the future for deprived children rather than simply masking the problem with state handouts that do nothing to get to the root of the poverty problem."
Government spent £170 billion between 2003 and 2010 trying to lift children out of poverty, but the targets forced politicians to focus on short-term income redistribution, rather than trying to help and support parents into employment or higher wage jobs, said the report.
Responding to the report, Mr Duncan Smith said: "This is exactly why we are consulting on a wider measure to capture the root causes of poverty, which include worklessness, educational failure and family breakdown. It is not just about money. Despite billions of pounds being paid out in tax credits in the past decade, the focus on income alone has not transformed people's lives. To have any real impact on tackling child poverty, we have to have a better understanding of what it means to live in poverty in the first place."