They said that a senior law lord had allowed a "real danger of bias" into the earlier hearing because of his long-standing links with the human rights pressure group Amnesty International.
The law lord, Lord Hoffmann was also accused yesterday of having been "an active and hostile interrogator" of General Pinochet's counsel.
The lawyers asked a panel of five senior past and present law lords to rescind the earlier panel's decision of 25 November to overturn the High Court's ruling of immunity.
It was Lord Hoffmann who cast the deciding vote which cleared the way for the Home Secretary, Jack Straw, last Wednesday to authorise that the 83-year-old face an extradition process launched by Spain onhuman rights charges.
Clare Montgomery QC, for General Pinochet, said that Lord Hoffmann's role in the decision and the "duration, variety and intensity" of his relationship with Amnesty gave rise to the "real danger of bias".
The human rights group had intervened in the original hearing and had argued against the general being protected from prosecution because he was the former head of state.
She said Amnesty must be considered "one of the principal protagonists in the extradition proceedings".
The Independent revealed yesterday that the general's solicitors, Kingsley Napley, received a letter 10 months ago relating to an appeal forAmnesty, which highlighted Lord Hoffmann's role. The firm had given pounds 1,000 in response.
Ms Montgomery said there was "some evidence" that both she and fellow Pinochet counsel, Clive Nicholls, should have known about the connection between Lord Hoffmann and Amnesty, but in fact they did not. Ms Montgomery referred to the report that some partners at Kingsley Napley should have known about the Hoffman-Amnesty relationship.
"I have been told that at a dinner given by, among others, Kingsley Napley, there had been on the table in front of me a similar letter to that received by the solicitors, requesting support for the Amnesty building," she said.
If, by seeing the letter there, she was taken to have known of the link Lord Hoffmann had with Amnesty then "I too am guilty of that."
She maintained that the onus of disclosure lay with Lord Hoffmann.
Alun Jones QC, representing the Crown Prosecution Service, argued that the general's lawyers had known of the links before Mr Straw's decision.
He said the general's lawyers had made the representations about Lady Hoffmann to the Home Secretary but they had been rejected.
Lord Hoffmann's wife, Gillian, is an administrative assistant at Amnesty and Lord Hoffmann is a director of thegroup's charity arm, Amnesty International Charity Limited.
Ms Montgomery said Lord Hoffmann had "authorised publication of a 1993 report on Chile, a report that was highly critical of Senator Pinochet."
However, the hearing was told that Amnesty denies Lord Hoffmann had played any part in any of its political campaigns.
Lord Browne-Wilkinson said the panel would not consider setting aside just the vote of Lord Hoffmann, thus confirming the High Court decision freeing General Pinochet.
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