An estimated 20,000 civilians were killed by North Korean-trained troops under the authority of current President Emmerson Mnangagwa, who was minister of security at the time.
The activists have asked Zimbabwe's High Court to compel Mnangagwa's government to release the findings of a commission of inquiry on the massacres.
Dumisani Dube, a lawyer for the pressure group Ibhetshu Lika Zulu, is hopeful despite previous unsuccessful attempts. He says the situation has changed in Zimbabwe since 2013, when a new constitution was enacted.
'In terms of the new constitution of Zimbabwe, section 62, there is a constitutional provision on the right to access to information, which entitles any person the right to any information which is held by the state in the interest of public accountability, fairness, human dignity and justice. So, we are very positive,' Dube said.
Ousted president Mugabe is cited in the court application, as it was his government which presided over the massacres between 1982 and 1987.
The atrocities targeted members of the ethnic Ndebele population believed to support former Vice President Joshua Nkomo, then an opponent of Mugabe.
Lawyer Dube said he would serve the papers to the British embassy in Harare for transmission to Theresa May's government in London. The pressure group wants the British government to release classified documents that might have details about the massacres.
Zimbabwe justice minister Ziyambi Ziyambi said he has yet to see the High Court application.
In a sign of growing tension over the massacres, the army recently detained and assaulted protesters demonstrating against a visit by Mnangagwa to the southern region.
The 75-year-old Zimbabwean leader has yet to comment on the issue since coming to power in November in an army-backed takeover.