He married Margaret Jackson in 1947. They met in Germany at the end of the war, and had one son and three daughters together. She died in 2003.
Davies became a judge of the Queen's Bench Division of the High Court of Justice in 1973, receiving the customary knighthood. As the senior High Court judge, he became Keeper of the Juries List in 1988, taking charge of the limited number of English civil cases - principally defamation cases - in which a judge continues to sit as arbiter of the law, with a jury as tribunal of fact. As a result, he sat on many high-profile cases, many of which were won by plaintiffs who were awarded ever large sums in damages. He was very active in managing the number and turnover of cases on the list, cutting the number of cases on the list from around 240 in 1988, when he was appointed, to only 50 cases two years later. The time before a case came to trial was also reduced from three years to only one. Davies was the judge in the case brought by Koo Stark in 1988, against newspapers that had claimed she had an adulterous affair with Prince Andrew. He was also the judge in a successful libel case brought in 1990 by Sonia Sutcliffe, wife of the Yorkshire Ripper, against Private Eye, which alleged that she had sold her life story to the Daily Mail. She was initially awarded then-record damages of £600,000 (reduced to £60,000 on appeal). Famously, Ian Hislop, editor of Private Eye, said on the steps of the court after losing the case: "If that's justice, then I'm a banana."
In 1990, he also presided over the libel case brought by Lord Aldington against Count Nikolai Tolstoy, in relation to allegations of bad faith in returning Cossacks to Stalin's Soviet Union and Slavs to Marshal Tito's Yugoslavia in 1945, at the end of the Second World War, which set a new record for libel damages of £1.5 million. He also sat on the libel case brought by Andrew Neil against Peregrine Worsthorne, in relation to a leading article in The Sunday Telegraph implying that Neil knew that Pamela Bordes was a call-girl before their affair in 1988, and in other cases involving celebrities such as Elton John, Tessa Sanderson, Linford Christie, Viscount Linley, Sir Ranulph Fiennes and Neil Kinnock.
As a judge, he could be charming and witty, and won praise for his clear explanations to the jury. He could also be grumpy and irascible, particularly when taking to task visitors his court who appeared in the public gallery for only a few minutes, as if his court was a public entertainment. His obituaries imply that he played to the jury, and tried to be the centre of attention, ticking off barristers who he thought were taking too much of his limelight. He was lampooned in Private Eye as "Mr Justice Cocklecarrot".
He was founding chairman of the Expert Witness Institute in 1996, and enjoyed reading, golf, theatre and opera, particularly the Welsh National Opera, and black and white films. He was a member of the Garrick Club.