Dubbed the Fallen Sparrow, the newborn's body was found in May 1982 in a carrier bag near Northampton railway station but for four decades has remained unidentified.
Despite a massive police investigation, the inquiry closed in 1993 but new evidence has surfaced after a cold-case review by officers.
Two weeks ago a woman, 57, was bailed pending further inquiries after being arrested on suspicion of murder.
Now Canon George Burgon, the retired vicar of St Mary's Church, Northampton, and wife Margaret hope the mystery may soon be solved.
They arranged the funeral six months after the little girl was found but it was attended by just three police officers, a gravedigger, an undertaker and two journalists.
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