Scott Snowden, 39, and Robert Jennings, 51, received sentences that were among the longest ever passed in Scotland after they were found guilty of the murders of Thomas Sharkey Snr, 55, his son Thomas Jnr, 21 - who was a promising golfer - and daughter Bridget, aged eight.

The pair were also convicted of attempting to murder Mr Sharkey’s wife, Angela, 48, who survived the fire.

Life sentences were handed down by the court and murder ‘mastermind’ Snowden was ordered to serve at least 33 years before he is eligible to seek release on parole. Henchman Jennings had a minimum term of 29 years imposed for carrying out the attack at the Scott Court home on July 24, 2011.

The pair raised challenges against their convictions and maintained that the trial judge did not give fair balance to defence and Crown when he came to address the jury at the end of the trial.

But judges at the Court of Criminal Appeal in Edinburgh have now unanimously rejected the challenges claiming there had been a miscarriage of justice.

The Lord Justice Clerk, Lord Carloway, said: “The whole tenor of this charge (address to the jurors by the trial judge) was one of balance.” The senior judge said: “The court is quite unable to sustain a submission of a lack of balance.” “No doubt the trial judge did not mention every point made by the defence in the speeches made on behalf of the appellants. It would not have been appropriate to do so, partly because such an exercise in itself may have been open to criticism as tarnishing the power of the speeches within the dramatic context of the trial as it developed live,” said Lord Carloway.

“A contention that a miscarriage of justice has occurred, which is supported only by pointing to a judge’s failure to mention a particular point or points raised by the defence, will not, of itself, suffice,” he said.

“The criticism must be a substantial one of imbalance going to the whole whole tenor or purport of the charge. Put simply, an appellant will require to demonstrate that, looking at the charge as a whole, its tenor was unbalanced in the sense of demonstrably favouring the Crown upon a contentious issue of fact raised in the trial,” he said.

Lord Carloway, who heard the appeal with Lady Smith and Lord Brodie, said: “The question then is one of whether, looking at the whole tenor or purport of this charge, the trial judge said, or failed to say, something which might have had the result of misleading the jury or diverting them from their task. The answer to that question is in the negative.” The Lord Justice Clerk said in this case a “very experienced trial judge” had been communicating with the jury.

“He was speaking to them in plain language; yet not patronising them with repetition of what they would already have well understood to be the issues in the trial,” he said.

Lord Carloway said: “The court is entirely satisfied that the judge achieved the appropriate balance.” The appeal judges rejected further grounds advanced by Jennings and commented that on one of them, over expert evidence of identification, that it was surprising that leave to appeal was granted.