The bombing of Pan Am flight 103, travelling from London to New York on December 21 1988, killed 270 people in Britain’s largest terrorist atrocity.
Former Libyan intelligence officer Abdelbaset al-Megrahi was found guilty in 2001 of mass murder and jailed for life with a minimum term of 27 years – the only person convicted of the attack.
In January, judges at the Court of Appeal in Edinburgh rejected a third appeal against his conviction, which was made by his son.
Lawyers acting for the Megrahi family then sought permission to appeal to the UK Supreme Court, but this was refused by five Scottish judges.
Aamer Anwar, the family’s lawyer, said they will now seek leave to appeal directly to the UK Supreme Court, the final court of appeal for the case.
A written judgment issued on Thursday by Lord Carloway, the Lord Justice General, said the court “has had some difficulty in understanding the exact nature of the challenge”.
It said: “Although the case is clearly one of public importance, the proposed grounds of appeal do not raise points of law of general public importance.
“The principles of law which the court applied were all well known, settled and largely uncontroversial in the appeal.
“For these reasons, the court refuses permission to appeal to the UK Supreme Court.”
Megrahi was released from prison in 2009 on compassionate grounds while terminally ill with cancer, and died in Libya in 2012.
The third appeal was lodged after the Scottish Criminal Cases Review Commission (SCCRC) referred the case to the High Court in March 2020, ruling a possible miscarriage of justice may have occurred.
Judges then granted his son, Ali al-Megrahi, permission to proceed with the appeal in relation to the argument “no reasonable jury” could have returned the verdict the court did, and on the grounds of non-disclosure of documents by the Crown.
Appeal court judges in January rejected both grounds of appeal, meaning his conviction stands.