Andy Burnham will call on the Home Secretary to support the introduction of a Hillsborough law to ensure the tragedy is a "watershed moment" for justice in Britain.
Labour are set to force two votes on Monday, seeing the Leigh MP ask MPs of all political parties to back major reforms to the policing and criminal justice system.
He will request support for parity of funding for legal representation for bereaved families, and the second stage of the Leveson Inquiry - looking at the relationship between the police and press.
The party will urge Theresa May to support a raft of amendments, including a Hillsborough Law to re-balance inquests, as the Policing and Crime Bill returns to the Commons.
Mr Burnham said: "The 27-year struggle of the Hillsborough families exposes how the odds are all too frequently stacked against ordinary families seeking truth and justice.
"Hillsborough must mark a moment of real change when Parliament rebalances the police and criminal justice system and puts more power in the hands of ordinary people.
"Never again should any bereaved families have to fight like the Hillsborough families have had to fight.
"We must call time on the uneven playing field at inquests where public bodies spend public money like water on hiring the best lawyers when ordinary families have to scratch around for whatever they can get."
Mr Burnham said if the families had had better legal representation in the early 90s they would have been able to challenge the "cruel 3.15pm cut-off".
The shadow home secretary added: "Public money should be spent on helping us get to the truth, not on protecting backs in the public sector.
"The Government made a clear commitment to victims of press intrusion and Parliament cannot let them renege on it.
"We need a full and thorough consideration of the relationship between press and police as recommended by Lord Leveson.
"After the Hillsborough verdict, Parliament has an unprecedented moment where it can act to rebalance the country in favour of ordinary families.
"I am calling on MPs on all sides to make Hillsborough a watershed moment for justice in Britain."