The Finucane family has renewed demands for a public inquiry into the murder following the conviction of Barrett.
Sir John Stevens, who headed three inquiries into the Finucane murder, said it was a "fair and painstaking investigation". He hoped it would bring "some sense of peace and closure" to the murdered solicitor's family.
However, Mrs Geraldine Finucane, who was shot in the ankle by her husband's killers, said yesterday's proceedings brought her "no peace and no closure".
"Our main priority has always been the people behind the gunmen who directed them, the people who directed the entire operation that seems to have been carried out in Northern Ireland for a long number of years.
"It's the policy makers that we want to hold accountable. This trial which did not take place today certainly brings us no nearer that truth."
Her son, Michael, told The Irish Times the main reason cited by the British government for not initiating a judicial inquiry had now been removed.
"The government should now set out the way ahead. When does the inquiry begin? Excuses and further prosecutions back up our fear of drip-feeding delays."
He said the British Prime Minister was obliged to act on his Weston Park commitments. "It's over to you Mr Blair."
Sinn Féin and the SDLP, backed the family's appeal and renewed their calls for an immediate judicial inquiry.
Sinn Féin's Mr Gerry Adams said: "This plea, in a move reminiscent of the trial of Brian Nelson, came about as the result of a sordid deal brokered by the British system to ensure that the collusion cover-up continues."
He accused "elements at the heart of the British system who manipulated and directed the activities of the loyalist death squads" of being determined that the full extent of their activities, including the Finucane murder, were not revealed in open court.
SDLP's Mr Mark Durkan said: "The British government has stonewalled all the way on this one, but the guilty plea by Ken Barrett removes the last stone. There must be no more excuses, no more ruses.
"At Weston Park Tony Blair made a solemn commitment to hold a public inquiry if Judge Peter Cory recommended that there should be one. Judge Cory so recommended, but the British government hid behind the excuse of a pending prosecution," Mr Durkan said.