Northern Secretary Hilary Benn has refused two further requests for public inquiries into Troubles murders.
The families of Kevin and John McKearney and Charles and Teresa Fox have been told their requests have been declined.
In January 1992, 32-year-old Kevin McKearney and his 69-year-old uncle John - known as Jack - were shot as they worked in their butcher's shop in the Moy, Co Tyrone.
In September that year, 63-year-old Charles Fox and his 54-year-old wife Teresa were gunned down in their home outside the village.
All four murders were claimed by the UVF.
State agents within the loyalist group have been linked to the murders.
Kevin McKearney's widow Bernie is a daughter of the Foxes.
In a letter to the families' legal teams, Mr Benn said he had weighed up a number of factors before reaching a conclusion.
"After due consideration, I have concluded that an inquiry under the Inquiries Act is not the best way to proceed," the letter stated.
"In particular, I consider the Independent Commission for Reconciliation and Information Recovery (ICRIR) to be capable of discharging the Government's human rights obligations."
Bernie McKearney said her family would not be giving up.
"Our inquest was stopped by the coroner and a public inquiry was recommended," she said.
"We want our inquiry and we are not accepting a lesser body like the ICRIR."
She promised to challenge the outcome in court.
The decision to decline the inquests follows a similar decision in respect of GAA official Sean Brown, who in 1997 was abducted and murdered by loyalists, including some working for the state.
HIs family was also told to speak to the ICRIR.
It is a body set up under controversial legacy legislation which the current UK government has said it intends to replace.
But the Northern Secretary seems intent on retaining the commission which was established under the act.
It has a truth recovery function and can also carry out investigations into Troubles’ era killings.
The appeal court in Belfast tomorrow is expected to hand down judgement in a case taken by families challenging its legitimacy.
A lower court found the commission could carry out investigations compliant with human rights legislation.
A number of families have contested that.
Last week, the British government announced it was prepared to hold a public inquiry into the murder of Belfast solicitor Pat Finucane.
That delivered on a 20-year-old British promise to the Finucane family and agreements reached with the Irish government as part of the peace process.
