Claire Throssell, 44, said she felt “very emotional” as she delivered the 40,000-signature petition but that “hopefully now children’s voices will be heard.”
The petition calls for an end to unsafe contact.
Ms Throssell urged officials not to assume that all contact by someone who is accused of domestic abuse will be safe.
Her sons Jack, 12, and Paul, nine, were killed by their father in October 2014 after he was granted unsupervised access to them.
Ms Throssell, of Penistone, near Barnsley, South Yorkshire, also helped to lay a memorial tribute of 20 teddy bears in Parliament Square.
It was to remember the children who have been killed through unsafe contact with an abusive parent in England and Wales since 2005.
Ms Throssell had promised her dying boys that she would work to try to keep other children safe.
She said: “No other child should have to suffer in the way that they had and also that no other parent should have to hold their child in their arms and watch them die, knowing it had been at the hands of someone who should have cared and loved them. All we have got is hope. If we do not have hope we have nothing, and then how can anything change.”
Her boys were killed in a fire set by their father, Darren Sykes, at his home in Penistone.
During divorce proceedings he had been granted access to his children for five hours a week, despite Ms Throssell’s evidence that he had previously threatened to kill them and himself. Sheffield coroner Christopher Dorries recorded a verdict that Mr Sykes, a 44-year-old salesman, committed suicide and that the two boys were unlawful killed.
The inquest into the boys’ deaths heard they had been lured to their father’s home with a new model train set before Sykes set fire to the building.
Sykes and Paul died in the fire, while Jack died in hospital six days later.
Ms Throssell is backed by Women’s Aid.
In a statement, actress Julie Walters, who is a Women’s Aid patron, said: “It is deeply shocking that the deaths of all of these 20 children were avoidable.
“The safety and well-being of children should be at the heart of every single decision made by the family courts. Unsafe child contact with unsafe parents must end.”
Louie Herbert, of the 38 Degrees campaign which helped set up to the petition, said the issue “has to be addressed, and quickly before another child dies in these horrific and avoidable circumstances.”