Mr Brown, the former Labour prime minister, ordered the creation of the Hillsborough Independent Panel, which in 2012 went on to reveal police failings and eventually led to the quashing of the accidental verdicts from the first inquests.
Speaking on Friday at the online Hillsborough Law Now event, Mr Brown said: “No one should be kept in the dark by bureaucratic indifference and deceitful lies like your families were kept in the dark.
“I say that an injustice anywhere is a threat to justice everywhere and to protect all, we need the Hillsborough Law now.”
‘Families denied access to justice’
Mrs May, the former Conservative prime minister, said bereaved families suffered “injustice heaped on injustice” following the tragedy.
“I have been struck in the case of Hillsborough, but in other cases too, at the way in which the state in its various forms acts to defend itself from blame,” she said.
“The very bodies that we expect to protect and support the public seek instead to protect themselves, and this defensive attitude means that families are all too often denied access to the truth and with that often denied access to justice.”
Steve Kelly, who lost his brother Michael in the tragedy, said: “A Hillsborough Law will allow ordinary people the same opportunity for legal representation from the beginning.
“I never want to see anybody go through this ever again, especially without support from the outset.”