A man and a woman have been sentenced to life imprisonment with a minimum term of 14 years each for murdering a vulnerable young woman, who they should have been caring for, almost two decades ago.

Margaret Fleming, who had learning disabilities, vanished “from the face of the earth” in December 1999. Her body has never been found.

Edward Cairney, 77, and Avril Jones, 59, were sentenced at the high court in Glasgow by the judge, Lord Matthews, after being found guilty of murdering the missing woman following a seven-week trial.

Jones was also convicted unanimously of fraudulently claiming £182,000 in benefits by pretending Fleming, who would now have been 38, was alive. The couple were both convicted of perverting the course of justice.

The judge sentenced the couple to life imprisonment, which is mandatory for murder, with both ordered to spend 14 years behind bars before they are able to apply for parole.

Matthews said: “You were convicted after trial of the murder of Margaret Fleming. Precisely how that was accomplished and any other circumstances was not disclosed in evidence and only you two know the truth. Only you two know where her remains are.

Facebook Twitter Pinterest Margaret Fleming. Photograph: Crown Office/PA

“That remains a source of immense grief as far as her mother is concerned. It seems obvious that the motive for the murder and cover-up was financial.”

The judge added: “Margaret Fleming was a vulnerable young woman with evident difficulties. She was in your care and you breached the trust placed in you. The manner in which you spoke about her was cruel. The fantastic web of deceit that you spun was callous and calculating.”

Lawyers for Cairney and Jones said both maintained their innocence. Thomas Ross QC, representing Cairney, said: “Mr Cairney continues to deny any involvement in the crime. He maintains that to his knowledge Margaret is still alive.”

Ian Duguid QC, representing Jones, said: “She, like Mr Cairney, denies her complicity in any wrongdoing in relation to Miss Fleming. She, like Mr Cairney, maintains that the young lady remains alive or at least until 2017, when the last opportunity arose for them to have any contact.”

The senior police officer investigating the case, Det Supt Paul Livingstone, urged the couple to reveal where Margaret’s body was. He said: “Margaret’s family and friends will never know just what happened to her and they have been denied the right to pay their final respects to her at her funeral.

“I would say to Cairney and Jones: if you have a scrap of decency you will give the answers to the questions that Margaret’s family deserve. I am willing to meet either of them so that they can tell me in order to provide some kind of comfort to her family and allow them to put her to rest finally.”

He said the case would “always be unfinished” for the police until Margaret’s body was found, adding he hoped the “pressure of the guilt” in jail would lead her murderers to reveal where she was.

Livingstone added: “It’s beyond wickedness what they’ve done. To cover it up for this length of time and to still today maintain that charade that she’s still alive is beyond words.”

Jurors found that the couple murdered Fleming by unknown means between 18 December 1999 and 5 January 2000 at their home in Inverkip, Inverclyde or elsewhere in Scotland, and then tried to cover up the crime for almost 18 years.

Police launched an investigation after it became apparent in October 2016 Fleming was missing. Routine social services inquiries were said to have sparked concerns about her whereabouts.

It was claimed the last independent sighting of her was at a family event on 17 December 1999. Her supposed carers were arrested in October 2017.