THE family of the man convicted of the murder of Edinburgh book-keeper Suzanne Pilley has spoken of the "appalling injustice" of the case as a review of the conviction was granted.

Relatives of David Gilroy, 51, who is serving a minimum of 18 years for the murder of 38-year-old Ms Pilley, his colleague and former lover, said they hoped moves towards quashing the conviction would be made this year.

The Scottish Criminal Cases Review Commission has accepted an application for a review of the conviction which could mean a referral back to the High Court.

The Gilroy family said in a statement that the grounds for the review included in the application are "substantial".

They claimed there were "faults by all parts of the justice system".

The application the family submitted raises issues about the "gathering of evidence; disclosure practices; non-disclosure of evidence; evidence not used by the defence team at the trial; evidence not available at the trial; trial and appeal procedures".

The Gilroy family said: "The family remain supportive of David in his work to bring to the attention of the justice system the significant flaws in the case brought against him.

"He has now spent nearly three years in prison wrongly convicted of a crime which he did not commit.

"The family is concerned at the time which it is taking to get recognition of what they believe to be a serious miscarriage of justice involving faults by all parts of the justice system.

"David Gilroy's family and friends hope that 2015 will see significant steps taken towards quashing his conviction and ending this protracted period of appalling injustice in all their lives.

"The family will have nothing further to say at this time."Ms Suzanne Pilley and attempting to defeat the ends of justice in May 2010.

Ms Pilley had set off on her usual journey to work in Edinburgh city centre but never arrived.

Gilroy went on trial at the High Court in Edinburgh in February 2012 and was convicted of murder in March that year.

Experts will study the grounds for the review over the next eight months before deciding if it should be referred back to the High Court.

The jury in Gilroy's trial heard he was driven by jealousy, maintained a front of normality and embarked on a series of acts to cover up his crime.

He took Ms Pilley's body to a secret grave, believed to be in remote Argyll.

Married Gilroy, 51, has protested his innocence since the day Ms Pilley disappeared.

Last year, the Supreme Court in London refused his application to have his case reviewed.

The case made legal history when Gilroy became the first convicted killer to have his sentencing filmed for British TV.

Judge Lord Bracadale told him when he was convicted that he hoped he would one day say where he abandoned the victim's body.

Few applications for review, usually made after other appeal processes are exhausted, are accepted by the SCCRC and a small percentage of those are referred back to the High Court.

Applications for review will only be accepted if grounds for appeal differ from any earlier legal bid.

A spokeswoman for the Justiciary of Scotland said it would be inappropriate to comment.

Niall McCluskey, QC, a human rights expert, said the commission will examine all the issues raised by Gilroy "and it is within their remit to decide whether it goes back before the court".