Members of Mothers' Union marched along Whitehall with placards before delivering the document which calls for a cost on child maintenance payment services to be waivered for all domestic abuse victims.
Speaking to Premier's Alex Williams outside Downing Street, Chief Executive Officer, Bev Jullien, said: "The problem is that at the moment there's a charge - based on average income - of £130 per child in order to access the service.
"That will be beyond the means of some people which would cause them to take alternatives measures and put themselves at risk."
According to Mother's Union, statistics reveal one third of Child Maintenance Service applicants has experienced domestic abuse.
Single mum Jackie told the Mothers' Union: "I have been in that position, and it can be hard to manage on a limited income.
"My ex told social services that he gave the children pocket money and this amount was promptly taken from my support. I lost out and he thought it funny".
Delivered to Downing Street on Friday and signed by 4,500 Mothers' Union members and supporters, the petition forms part of a new campaign trying to tackle domestic violence around the world.
The #itsnotok campaign wants governments around the world to move towards eradicating the problem, and for survivors to have access to justice and support.
Click here to hear Bev Jullien speaking with Premier's Alex Williams: