A series of intelligence reports and other files relating to the miners' strike, previously held by the now-defunct Association of Chief Police Officers (ACPO), are categorised as containing "personal sensitive information" and closed until 2066.
Home Affairs Select Committee chairwoman Yvette Cooper has written to Home Secretary Amber Rudd, asking her to set up a review of the files to see whether they can be released, with redactions if necessary.
She said there could be "no more secrets or cover-ups" about what happened.
The Government has ruled out holding an inquiry into the events at Orgreave in South Yorkshire in June 1984.
Scores of miners were charged over the violence, and many were injured, although all charges were later dropped.
Labour MP Ms Cooper said: "People want to know the truth about what happened at Orgreave, especially in the coalfields.
"Little by little, our questions are uncovering what files and information are still held. Some of the intelligence files we have identified are being withheld until 2066. We have asked the Home Secretary to get those files independently reviewed to see if they can be released instead."
The committee contacted 18 forces that contributed to policing at the Orgreave coking plant in June 1984 as well as the National Police Chiefs' Council, which replaced ACPO.
The Metropolitan Police were asked if they held the operational policing plan for the day on which the confrontation took place, but Scotland Yard said operations on the day were led by the local force in Orgreave, South Yorkshire Police.
Ms Cooper said: "This correspondence also confirms that most of the Orgreave files are still with South Yorkshire Police. That means the most important thing is for those files to be properly reviewed and made public too.
"People in coalfield communities need to know what happened at Orgreave and deserve access to the truth. There must be no more secrets or cover-ups. That is why we keep pushing to get to the bottom of this."