Extradition rulings against Pinochet were challenged on the basis that one of the law lords, Lord Hoffmann, had links to Amnesty International, which had presented evidence to the court on the side of the crown. As a result the decision was quashed and re-heard by a new bench of 7 judges. This was despite the fact that neither Pinochet nor other judges considered that Hoffmann actually was biased.
Lord Browne-Wilkinson: The basic principle is that a man may not be a judge in his own cause. He says that this leads to automatic disqualification where a party has a financial or proprietary interest in the outcome of the case or is a party to the case (including if he has a “relevant interest in the subject matter”). This causes disqualification without investigation, unless the judge declared his interest, into whether there was actual bias. Lord Hoffmann fits this category, because of his involvement with Amnesty International, who were a party to the case.