Saskia Jones's mother Michelle Jones said she wants new legislation to help "avoid another family being torn apart in similar circumstances".
They were stabbed by convicted terrorist Usman Khan during a prisoner rehabilitation event.
In a statement released through the Metropolitan Police, Michelle Jones said she is working to create several legacies in Ms Jones' name "that could be the foundation of improving the lives of others from the many causes she supported".
She said: "Although it is early days, we will also be taking part in consultations to launch a new law (security legislation) for businesses and operators of public spaces who hold events.
"This legislation will ensure that proper security measures are in place to avoid another family being torn apart in similar circumstances."
Khan, 28, was out on licence when he attended the event armed with two kitchen knives and wearing a fake suicide vest.
He was tackled by members of the public with a narwhal tusk, a decorative pike and a fire extinguisher before he was shot dead by police on London Bridge.
The statement was issued as Ms Jones and Mr Merritt were commemorated on the one-year anniversary of the attack on Sunday.