Sir Keir praised Ms Aspinall’s “courage” and “the strength of all the Hillsborough families and survivors” in their long campaign for justice.
He said the new legislation would change “the balance of power in Britain” to ensure the state could “never hide from the people it is supposed to serve”.
“Make no mistake, this a law for the 97, but it is also a law for the subpostmasters who suffered because of the Horizon scandal, the victims of infected blood, and those who died in the terrible Grenfell Tower fire,” he said.
One of the bill’s architects, Elkan Abrahamson of law firm Broudie Jackson Canter, said there was still some way to go before it became law.
“We will now scrutinise the bill as it makes its passage through parliament, so we’re not quite there yet,” he said.
“But today is still a momentous step, owed entirely to the persistence of campaigners and their refusal to give up.
“The Hillsborough Law will transform the face of British justice.”