Peter Fell, of Great Harwood, spent more than 18 years behind bars after two women were killed on Aldershot Common, close to where he was based in the Army, in 1983.
He has been asking Hampshire Police and Chief Constable Paul Kernaghan to find the murderer since being released by the Court of Appeal in 2001.
But today the force - which last year spent money on mountain bikes for officers and Christmas cards wishing criminals a crime-free new year - said it did not have the resources to re-investigate the case.
It said t it had more important things to do than try and find the killer of Ann Lee and Margaret Johnson.
Hyndburn MP Greg Pope said the decision "beggared belief" and that police had mishandled the case from start to finish.
Mr Fell, who was brought up in a Great Harwood children's home and went to Norden High School, Rishton, said: "I have asked and asked and asked Hampshire Police what they are doing with the case but they keep telling me they cannot afford to do anything with it.
"I think that's wrong, because there is still someone who killed wo women out there and for as long as they do nothing about it, they might as well be saying 'I think you did it'.
"There are several things holding me back from getting on with my life, and one of the things is the fact they aren't investigating the case.
"They haven't apologised for what they did. I retracted the confession I made three hours after I made it, but they pressed on and I lost 18 years of my life as a result."
Mr Fell, who has now married and lives in Essex, was released "without a stain on his character" by appeal court judges sitting in London after they were told jurors at the original case had not been informed of vital information.
Mr Fell initially admitted the killings when interviewed by police, but jurors were not told during his trial that he was suffering from a condition which made him a "pathological confessor".
The 43-year-old, who still has family living in Hyndburn, now claims to be suffering from post-traumatic stress caused by the manner of his release from prison.
During his four-day appeal hearing, heard in London, the court was told detectives at the time had behaved in a 'reprehensible' manner. Hyndburn MP Greg Pope said: "Hampshire Police have mishandled this case from start to finish.
"They have been appalling. It beggars belief that after a man has been imprisoned for 18 years for a crime he did not commit they cannot be bothered to catch the real perpetrators of this evil crime.
"It should be a priority because there is a double murderer out there. Advances in forensics technology should be enough to reinvestigate the case."
A spokesman for Hampshire Police said: "The case will only be investigated if further evidence comes to light. It is not a priority and we have to judge cases against our resources.
"There are more pressing cases."
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