Emma’s mother, Margaret Caldwell, said: “I’ll go on as long as it takes. I need to be able to trust [in the inquiry], and have truth – that’s all I’m asking for.

“As the mother of Emma, I’m appealing to Lord Pentland – please, let it be an independent judge.”

Ms Caldwell said it was “very difficult” to hear that more patience was required. She added: “I’m not waiting any longer. I need justice for all those years I’ve been lied to.”

Mr Swinney said: “I am very grateful to Mrs Caldwell for meeting with us. It was my first opportunity as first minister to express my deepest condolences to her on the death of Emma, and the trauma she and her family have experienced. The family have endured heartbreaking loss, pain and grief for many years and they have shown immense courage in their determination to get justice for Emma.

“As announced in March, an independent, judge-led, statutory public inquiry will take place into the investigation of Emma’s murder in 2005. The justice secretary and I had the opportunity to listen to the family’s views on next steps, including the appointment of a chair and ways to progress the investigation of the initial police inquiry. We appreciated their time and views, which allows us to move forward with the work to be done ahead of establishing the Inquiry. It is vital that the chair has the confidence of the family and we will continue to engage with them on this.”

A Police Scotland spokesperson said: “We have been clear that we will fully support any further police investigation into the murder of Emma Caldwell and also the work of the Crown Office and Procurator Fiscal Service to identify an external force to carry out this significant piece of work.”