Margaret Aspinall, whose 18-year-old son James died in the disaster, said: "After hearing the stories of all the other families fighting for justice, I am more determined than ever to demand that the Hillsborough Law presented to Parliament is all or nothing."
Inquest has published a report after bringing together "powerful voices of bereaved families, victims and survivors of some of the worst failings of public services and the legal system in the UK" to re-state the need for a strong law.
In it, Ms Coles said the law "must be 'all or nothing', without dilution or caveat, to ensure the response to contentious deaths, harms and grave injustices dramatically improves".
Grenfell United's Natasha Elcock said "so many institutions and companies" had tried to protect their reputations following the 2017 west London tower block fire which claimed the lives of 72 people.
She added: "Why is it so easy for public and private agencies to escape accountability and scrutiny?
"Establishing a duty of candour could prevent this, help us learn from failures and ensure bereaved and survivors are properly supported. This is why a Hillsborough Law is so urgent."
Speaking in Parliament last week, Ms Powell said the "most important issue at this time is to ensure that the legislation reflects the full range of concerns and experiences, and meets the expectations of the families".
She added: "I think the very worst thing we can do at this point in time is to not meet those expectations when all of the trust and issues there are about the state failing to live up to those expectations of the families.
"So we are working on the bill at pace, but we will take whatever time is necessary to work collaboratively with the families and their representatives."