In doing so, an earlier Court of Appeal decision to ramp his sentence up to 18 years from the originally imposed term of 13 ? years was upheld.
Beckham appealed against that increase on the basis the Court of Appeal wrongly applied the test for sentence reduction as a remedy for police misconduct in breaching the Bill of Rights Act.
His appeal said those breaches happened when police obtained copies of recordings of phone calls
Beckham made when he was a remand prisoner, including to his trial lawyer Murray Gibson.
Beckham's bid to appeal against his convictions was also made on that basis.
Beckham's lawyer Simon Mount told the Supreme Court those calls gave police insights into discussions that were legally privileged.
Communications between Beckham and his partner and son were also listened to, and some of those referred to legal matters.
However, the Crown said most of those calls were about "simply keeping in touch and discussing normal domestic and business matters, rather than preparation for trial".
The Crown also said that Beckham made the calls in question from a phone prisoners knew was monitored.
In today's judgment, Justice Mark O'Regan said the police officer in charge of the case, Detective Sergeant Jason Lunjevich, should have excluded Mr Gibson's number when applying to the court for a warrant to obtain copies of Beckham's calls.
"It is simply unacceptable for a police officer to seek a warrant that would involve seizure of privileged calls between a remand prisoner and his lawyer and equally unacceptable that the judicial officer who issued the warrant was not made aware of the situation."
But, when monitoring Beckham's calls, police did not listen to anything covered by client privilege and the Supreme Court concluded allegations against police were over-stated, as was any impact on Beckham.
"The suggestion that privileged information came into the hands of prosecutors at Mr Beckham's trial, with the implication that his fair trial right was affected, is not borne out by the evidence," Justice O'Regan said.
The court ruled the process police and Customs officers undertook to obtain warrants to seize or listen to calls was defective, the warrants were unlawful and the seizure of privileged material was in breach of the Bill of Rights.
But no evidence called at Beckham's trial was based on the privileged material.
"We consider that the argument that the trial was an abuse of process fails on the facts," Justice O'Regan said.
The breaches suffered were "adequately remedied" by granting Beckham bail ahead of his trial.
Justice O'Regan heard the appeal alongside Justices Terence Arnold, Susan Glazebrook, William Young and Chief Justice Sian Elias.
