Charity Gingerbread, which supports single parent families, said if those owed maintenance and living in poverty nationally were paid what was due, three in five would be "lifted out of the poverty trap".
While separated parents can agree a child maintenance arrangement, many use the Government's Child Maintenance Service to calculate how much one parent should pay to the other for their child's upbringing.
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Parents can be forced to use the CMS s Collect and Pay Service if they cannot agree a sum or someone has not kept up the payments.
Department for Work and Pensions data shows 79 parents in Crawley failed to pay any child maintenance through the Collect and Pay service between January and March.
It means 25% of the 310 single parents using this service, paid no maintenance over the three-month period.
The figures also show seven parents only paid up to 30% of what they owed their former partner, while 20 paid between 30% and 60% of what was due.
Across Great Britain, 42,000 parents did not pay any child maintenance they owed in the three months to March – 28% of those using Collect and Pay.
The CMS is supposed to take money directly from someone’s earnings or their bank account if they try to avoid payment, and can eventually take them to court if necessary.
But between December 2020 and the end of March, overall arrears owed to children through Collect and Pay increased by £12.5 million.
Victoria Benson, Gingerbread's chief executive, said the CMS's enforcement was ineffective.
"The CMS allows non-paying parents to build up huge arrears with 42,000 parents not paying any of the child maintenance they owe under Collect and Pay.
"This means not only are single parents and their children forced to go without with many being pushed into poverty and debt, but it allows the continuation of economic abuse and control in abusive relationships."
The paying parent must also foot a 20% charge to use Collect and Pay, while the other sees 4% being deducted from what they receive.
Ms Benson said these fees penalise the children involved.
“Children are going without as a result of these fees being deducted and it simply cannot be right that a government service is responsible for this,” she added.
But the DWP said the fees were intended to provide both parents with an incentive to collaborate.
A spokesman said: "The CMS puts children first, with their work securing £249 million for British kids in the first quarter of 2021 as they use the full range of their powers to secure money from parents failing to face up to their responsibilities.
"The latest statistics show that a record number of parents are now paying over 90% of what they owe."
Since the Covid-19 outbreak, more parents are claiming benefits and therefore paying child maintenance as an automatic deduction from those.
DWP statisticians said this has been affecting the compliance rate since April 2020 and is likely to continue to do so for some time.