Pearse McAuley had been wanted in connection with IRA offences
Two men who shot their way out of Brixton prison in London in 1991 while awaiting trial on IRA charges will not be prosecuted.
The Crown Prosecution Service said there was "no realistic prospect" of convicting Pearse McAuley and Nessan Quinlivan.
The move was announced as McAuley from Strabane, County Tyrone, was released from prison in the Irish Republic.
Two other suspected IRA men will also not be pursued.
The CPS said it had advised the Metropolitan Police that it would no longer be seeking the extradition of the four men from Ireland: Nessan Quinlivan, Pearse McAuley, Andrew Martin and Anthony Duncan.
It said it had considered evidence as well as the likely arguments which would be put forward by the defence, who would argue that an abuse of process had occurred so a trial could not go ahead.
The CPS said one of the probable defence arguments it considered was "statements made by ministers in respect of terrorists on the run."
Having reviewed the cases, the CPS decided there was no longer a realistic prospect of conviction.
This means that an extradition can no longer go ahead and the extradition requests to the Irish authorities will be withdrawn.
Before their escape Nessan Quinlivan and Pearse McAuley were being held for conspiracy to murder the brewer Sir Charles Tidbury and conspiracy to cause explosions.
Attempts to return them to England for trial stretch back to the mid-1990s.
On Wednesday McAuley was freed from Castlerea prison where he had served a sentence for killing Detective Garda Jerry McCabe during an armed raid on a post office van in County Limerick, in 1996.
Anthony Duncan was wanted for questioning over bombs attached to bicycles in Brighton and Bognor Regis in 1994.
Andrew Martin was wanted on bomb making offences and conspiracy to cause explosions.
He was identified as a suspect in 1995 and arrested in 1998. In 2001 he was successful in appealing against extradition.
Sinn Fein have welcomed the move but Jim Allister of Traditional Unionist Voice described it as "nothing short of outrageous".
Jeffrey Donaldson of the DUP said Ulster Unionist Party policies had led to the move.
"These terrorist criminals who shot their way out of Brixton Prison are now enjoying the benefits of policies enacted by David Trimble and Reg Empey.
"Thanks to the Belfast Agreement, which the UUP negotiated and implemented, terrorists were released from prison and even if these men were extradited and convicted it is likely that they would never serve a day in jail."
Sir Reg described Mr Donaldson's criticism of the UUP as "absurd" and called for the CPS to present the detailed reasoning behind their decision.