Judge Topolski QC has said he would not pass sentence on the two men until a Court of Appeal decision about a similar case had been heard later this summer.
However, sentencing is due to open this afternoon.
The judge earlier told the court that he was willing to offer a reduction in sentence if the defendants were to plead guilty.
He described the case as a "grave one".
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Detectives in Westminster are investigating after the man was discovered on the Route 189 bus in Marylebone shortly after midnight.
The murderer was shaking and appeared to be gasping for air for around 13 minutes before dying.
The positive results come after Chancellor Philip Hammond admitted the government is prepared to sell its stake at a loss to the taxpayer.