Dominic Grieve was giving evidence to the NI Affairs Committee as part of its inquiry into the On the Runs scheme.
Under the On the Runs scheme, letters were sent to around 200 republicans telling them they were not wanted by the police.
John Downey, who lives in Ards, Creeselough, was mistakenly sent a letter telling him he was not wanted for questioning by the PSNI or any other UK police force.
The PSNI later discovered that he was in fact wanted in connection with the 1982 IRA bombing that killed four soldiers, but did not correct the mistake.
In February, a judge at the Old Bailey in London said that meant a decision to prosecute him amounted to an abuse of process, and ruled that he could not stand trial.
Questioned by the Northern Ireland Affairs Committee yesterday, the Attorney General for England and Wales said there were no grounds for an appeal.