The director says, Ink on the tabloid under Rupert Murdoch, points out the terrible mistakes it made.
The prime minister says he will do his "own communications", differently to others in the past.
The UK Football Policing Unit later said it had not intended to link alcohol consumption with the Hillsborough disaster.
The former home secretary says he regrets not having done more for the Hillsborough families.
Liverpool mayor Steve Rotheram says "lots of unsung heroes" fought for the law to help other people.
The long-delayed legislation - formally known as the Public Office (Accountability) Bill - is expected to become law by the autumn. Ninety seven Liverpool fans died as a result of the crush during the FA Cup semi-final at Hillsborough in 1989. The Hillsborough Law would create a legal duty for public officials to tell the truth to inquiries and investigations.
The legislation cleared the House of Commons in Sir Keir Starmer's final days as prime minister.
The Hillsborough families celebrate the landmark Hillsborough Law finally clearing the Commons.
The crush at the 1989 FA Cup semi-final between Liverpool and Nottingham Forest left 97 fans dead.
