But now, Lord Bingham - who has never sat as a law lord - moves into the top job over the heads of the other judges.
Lord Bingham is the first person to be directly appointed as the top law lord to hear appeals from throughout the United Kingdom.
Lord Woolf becomes Lord Chief Justice of England and Wales, the post which Lord Bingham vacates.
Until now the job of senior law lord has gone to the judge who has been there the longest.
But now, Lord Bingham - who has never sat as a law lord - moves into the top job over the heads of the other judges.
There has been no explanation for this innovative move from the Lord Chancellor, Lord Irvine, who recommended his appointment.
But the reputation of the existing law lords took a battering 18 months ago when Lord Hoffmann heard the first Pinochet appeal while disqualified from sitting.
Also, the role of the law lords as the final court of appeal will become increasingly important once the Human Rights Act takes effect throughout United Kingdom in October.
The Act meets the government's manifesto commitment to incorporate the European Convention on Human Rights into UK law.
Rights enshrined in the Act include the right to liberty and security, the right to a fair trial, the right to freedom of thought, conscience and religion and the right to freedom of expression.
It also prohibits discrimination.
Bulger killers
Lord Woolf moves up from Master of the Rolls to Lord Chief Justice of England and Wales.
One of his first jobs will be to decide how long the two boys who murdered James Bulger should serve in custody.
Robert Thompson and Jon Venables were jailed for life at Preston Crown Court in 1993.
The trial judge recommended a minimum sentence of eight years and the then Lord Chief Justice, the late Lord Taylor of Gosforth, suggested 10.
The matter was referred to Lord Woolf by Home Secretary Jack Straw after the European Court of Human Rights ruled that it was wrong for former home secretary Michael Howard to have set a minimum sentence of 15 years.