Stephen Miller, 26, Yusef Abdullahi, 30, and Tony Paris, 35, were sentenced at Swansea Crown Court in 1990, after the longest murder trial in Britain. Two other defendants were acquitted.
The Lord Chief Justice, Lord Taylor, sitting with Mr Justice Popplewell and Mr Justice Laws, quashed the convictions after ruling that Mr Miller's police interviews - which were all on tape - were 'bullying' and should not have been put before the jury.
'If you go on asking somebody questions, even if he is not particularly susceptible, and tell him he is going to sit there until he says what you want, there will come a time when most people will crack,' Lord Taylor said.
To cheers from the men's supporters, Lord Taylor said the court would give its reasons for the decision next week. Outside the court the three men vowed to fight for other innocent prisoners.
Ms White, 20, was murdered in her 'punters' room' at Butetown, Cardiff, on St Valentine's day, 1988. She had been stabbed more than 50 times. None of the plentiful scientific evidence in the room pointed to the convicted men. Although Mr Miller denied the murder more than 300 times, he confessed after five days in custody and 19 police interviews. Michael Mansfield QC, for Mr Miller, described the police interview technique as 'beating him over the head verbally'.
Lord Taylor said that if the tapes should not have been admitted at the trial in which all three men were accused, none of the convictions could be upheld.
Gareth Peirce, Mr Miller's solicitor, said the case highlighted concerns that the 1984 Police and Criminal Evidence Act (Pace) was failing to provide safeguards for suspects. 'The interviews with Mr Miller were recorded as required under the provisions of Pace, but he was still convicted.'
Robert Lawrence, Chief Constable of South Wales, said: 'All confessions by Stephen Miller were made in the presence of his solicitor. It was always recognised that the validity of the confessions would be a matter of opinion, and they had already been the subject of scrutiny in two trials before two different presiding judges.'
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