The money is owed by non-resident parents and has built up over 23 years, with figures showing about 1.2 million people are owed child maintenance.
The Department for Work and Pensions said a new system was "actively pursuing" unpaid child maintenance.
But Janet Allbeson, from the charity Gingerbread, called for parents waiting for money to receive compensation.
The latest figures, revealed by the Victoria Derbyshire programme, show the vast majority of unpaid maintenance money was accumulated under the Child Support Agency (CSA) - which was set up in 1993.
The system was replaced in 2012 after mistakes were made with assessments and absent parents were not tracked down.
However, a further £93m of unpaid child maintenance has already developed under the new Child Maintenance Service (CMS) system.
It comes as the findings of a Work and Pensions Committee inquiry into CMS are due to be published next week.
MPs on the committee are expected to be highly critical of the new scheme.
Laura Riley, from Sheffield, has a 10-year-old son, Louis. His father has been assessed by the CSA and should be paying child maintenance.
However, Laura says she has been chasing money for nine years and that he now owes more than £9,000.
"At the beginning when I first moved up to Sheffield it was really tough because I just didn't have the money to look after [Louis] properly," she said.
"Instead of doing fun things I'd just take him to the park, with the same picnic every day and a book. I did my best, but I would have liked to have done more.
"I've sent letters and letters. At one point, I sent one every single week," she added.
"It's been a massive headache. I just felt like I was getting fobbed off to be quite honest.
"They asked for bank details, said they'd get the money off him and put it in my bank, and it just never happened. It's been like a massive battle for years trying to get the money out of him."
Louis's father is Gary Lawford, a children's entertainer in Brighton.
She says attempts to get money from him have proved to be "completely unsuccessful", adding: "I've realised it's not quite as easy as you think."
The CSA has taken enforcement action on three occasions, but they have not been able to recover any money.
"As his father, he has a responsibility. You don't just have the child; you raise them, you support them, and he's not doing that," she added.
The Victoria Derbyshire programme contacted Mr Lawford about the allegations but he declined to comment.
When couples split up, they are both still expected to contribute towards the upbringing of their children.
If parents can't agree how much one should pay, a government agency decides on child maintenance.
The Child Support Agency was set up in 1993 to ensure that non-resident parents contributed towards the cost of bringing up their children.
However, it was dogged by problems and has since been replaced with the Child Maintenance Service.
CMS - which was introduced in 2012, with new IT systems designed to improve the system - assesses the parents on a range of measures.
Payments are based on a standard formula, and CMS also collect payments for the receiving parent.
Child maintenance is payable for children who are under the age of 16, under 20 and in full-time education at A-level stage or below, or if they are under 20 and living with a parent registered for child benefit.
Unpaid child maintenance can be collected by taking money from a paying parent's earnings or benefits, directly from a parent's bank or building society, or through court action.
Source: Department for Work and Pensions
Janet Allbeson, from the single parents charity, Gingerbread, said powers to collect child maintenance are "very seldom used", saying CMS was "a very blunt instrument".
She said the uncollected figure was "a huge, startling number".
"People can't quite believe it, and do a double take. And it's money that's built up over a long time."
The charity says there should be compensation, paid by the government to children and their families who have lost out.
"They shouldn't just be able to walk away and say it's history when it's due to their errors and their poor practice that money hasn't been collected. That's wrong and the government should pay for that," she says.
"At the moment there are still questions to be asked about how much effort is being put into chasing those who choose not to pay, and we don't think as yet they've got that right, and there's more that needs to be done," Mrs Allbeson added.
The Department for Work and Pensions said: "We actively pursue non-resident parents to recover unpaid maintenance and we are transferring existing arrears from the CSA to the CMS.
"The new system is designed to encourage parents to come to their own family-based arrangement."
It said in 90% of cases, parents "are paying towards the money owed".
Watch the Victoria Derbyshire programme on weekdays between 09:00 and 11:00 on BBC Two and the BBC News channel.
There is a UK backlog of more than £3.8bn in uncollected child maintenance payments, figures have revealed.