A fifth of seven-year-olds in the UK live in "severe poverty" with both parents together earning less than half the average national income, a major report reveals.

The government-sponsored Millennium Cohort Study has tracked 14,000 children born at the start of the century to build a picture of how family circumstances determine a young person's education, health and happiness in Britain. The latest findings are from two years ago, when the children were seven years old.

The London University's Institute of Education researchers found that despite governments having spent billions to eliminate child poverty since 1999:

• Almost one-fifth of seven-year-olds live in severe poverty – homes where the total income, including benefits, is less than £254 a week [this is an average among those surveyed]. The average income for families in the study was £563 a week, say researchers.

• Almost three-quarters of children whose parents are of Pakistani or Bangladeshi origin live in poverty – homes where the total income for a family with two children is under £330 a week. This is largely because of high unemployment rates for mothers and fathers, the researchers say.

• Just over half (51%) of black seven-year-olds and just over a quarter of white seven-year-olds live in poverty, with three-fifths from these groups in single-parent families.

• Seven-year-olds are most likely to live in poverty in the north-east (40%) and least likely in the south-west (22%). The figure for London was 36%.

• Just under 7% of seven-year-olds living in poverty do not have two pairs of all-weather shoes, according to parents. Just under 50% do not get pocket money.

The researchers interviewed the parents of the 14,000 seven-year-olds. They asked them to place themselves in one of 18 categories corresponding to their weekly family income. The interviewers also measured the children and gave them a questionnaire to complete which asked them how happy they were. They accounted for how many children were in each home.

The number of children living in poverty is likely to be rising, said Professor Heather Joshi, the study's director.

"Our study captures how things were in 2008. This is not encouraging for child poverty today because worklessness is the most common indicator of poverty and our unemployment rate has gone up since then. Poor housing, low levels of qualifications among parents and low family income tend to be the key indicators of disadvantage."

Mothers who had given birth aged 19 or younger and parents with no qualifications are heavily over-represented in the fifth of families living in severe poverty, while older mothers, who had given birth in their thirties, are over-represented in the richest fifth, where the weekly income averages £1,134. Scottish seven-year-olds are slightly more likely to be living in affluence. Welsh children are slightly more likely to be in poverty.

Just over half of mothers without any qualifications are in the poorest fifth, while 32% of fathers without qualifications are in this group. More than half of the mothers and fathers with postgraduate qualifications are in the top income group.

The researchers focused on the UK's most-deprived neighbourhoods but adjusted the weighting of their findings to reflect all parts of Britain.

Meanwhile, the study also found that just over half of the seven-year-olds – 55% – live with married parents in England. This rises to 61% in Northern Ireland but falls to 53% in Scotland.

The mothers of the seven-year-olds were asked to place their children's behaviour in one of three categories: normal, borderline and or serious behaviour problems. About 12% of children in single-parent families and 15% of children living with a step-parent were described as having serious behaviour difficulties. This is compared with 6% for children living with both of their birth parents.

• This article was amended on 15 October 2010. In the original, an average income of £563 was given as the figure for a UK family with one child. The study was said to have asked parents to place themselves in one of five income categories. A sentence said that in the top income group more than half of the mothers and father have postgraduate qualifications. This has been corrected.