MPs are calling for a Hillsborough-style inquiry into the death of Hilda Murrell, a peace campaigner who was abducted and murdered in 1984.
Andrew George was convicted in 2005 of the murder of the 78-year-old anti-nuclear campaigner from Shropshire.
A Commons motion claims there are "serious and substantial doubts about the criminal investigations".
It calls for all the relevant papers be published by the Home Office and West Mercia Police.
The motion backs calls by human rights lawyer Michael Mansfield QC for a commission of inquiry into the case along similar lines to the Hillsborough Independent Panel.
West Mercia Police spokesperson said: "We are satisfied with the policing and judicial processes which led to Andrew George being charged and subsequently receiving a life sentence, for murder."
The force said there are currently no new grounds for a further police investigation, but added it was not up to them to decide if a case of this kind should be reinvestigated.
"The correct procedure is to appeal to the Criminal Case Review Commission," the spokesperson added.
Twenty five MPs have signed the motion, which was tabled by Austin Mitchell, the Labour MP for Great Grimsby.
Miss Murrell, a prominent member of the Campaign for Nuclear Disarmament (CND), was sexually assaulted and stabbed in 1984.
Security services suspicions
George, a builder's labourer with previous convictions, was arrested and charged in June 2003, after his DNA was found to match samples taken from the scene.
Last year, Miss Murrell's nephew Robert Green relaunched a book claiming there was new DNA evidence from his aunt's fingernails, which could acquit George, who was 16 at the time of his aunt's death.
Members of her family have long believed the security services were involved because of her political work in opposing nuclear weapons," said the BBC's political correspondent, Paul Rowley.
Last year, barrister and legal campaigner Mr Mansfield described the security services as "major suspects".
The motion notes that Mr Green's book makes the claim "key forensic and other evidence was not disclosed at the 2005 trial and the 2006 appeal of Andrew George".
It adds that Mr Mansfield views the book as raising "serious and substantial doubts about the criminal investigations to date into this controversial case".