It is perhaps ironic that a lecture by a judge on when it might be appropriate for judges to speak to reporters should have remained unnoticed by reporters until two weeks after it was delivered. But then the Holdsworth club - the student law society at Birmingham university - is so effective at avoiding publicity for its annual lecture that Lord Neuberger, who spoke earlier this month about when judges should speak out, did not appear to know that his judicial colleague Lord Hope had chosen the same topic for his own Holdsworth lecture just two years earlier.

The master of the rolls and the deputy president of the Supreme Court reach similar conclusions in their respective lectures, though by different routes. Neuberger starts with the Kilmuir ‘rules’ - no more than a letter written in 1955 by the lord chancellor to the BBC director general - in which Kilmuir famously asserted that ‘so long as a judge keeps silent, his reputation for wisdom and impartiality remains unassailable; but every utterance which he makes in public, except in the course of the actual performance of his judicial duties, must necessarily bring him within the focus of criticism’.

Kilmuir’s effective ban on broadcast interviews with serving judges remained in force, as I well remember, until it was abolished by Lord Mackay of Clashfern shortly after he became lord chancellor in 1987. That said, it is still the view at the very highest level of the judiciary in England and Wales that judges, even senior judges, should not take part in radio programmes such as Law in Action, which I present for the BBC. But, as Kilmuir recognised, individual judges can make up their own minds - which is how I get my interviews.

Neuberger offers an important gloss on Kilmuir’s thesis, albeit parenthetically. He points out that judges who speak publicly about matters of political controversy are then precluded from taking part in related judicial proceedings. But what if the judges who happen to have strong views on specific topics choose to keep quiet about them? It may be ever more pernicious for a judge with private opinions on a subject to decide an appeal in which those issues are raised, Neuberger suggests. He finds ‘obvious force in the argument that the presently accepted approach discourages transparency and encourages hypocrisy, or, to put the point another way, the present system seems to value justice being seen to be done above justice actually being done’.

In calling for ‘reticence, not absolute silence’ from his fellow judges, Hope mentions two cases that might come within these strictures. The first involved Lord Phillips, who retires this year as president of the Supreme Court. Giving a newspaper interview in 2009, Phillips admitted being a supporter of assisted suicide. He had already given his ruling in the Debbie Purdy case, brought by a woman who was seeking assurances that her husband would not be prosecuted if he helped her to die. So what was the problem?

Having read Phillips’s comments, campaigners sought to have the Purdy decision set aside on grounds of his apparent bias. Their application was summarily dismissed as having no reasonable prospects of success. But, as Hope says, the case reminds us ‘how careful judges must be in what they say even after the case is over’.

Sometimes a judge may face problems despite saying or doing nothing at all. That was the fate of Lady Cosgrove, a Scottish judge who had dismissed an asylum appeal brought by a Lebanese supporter of the Palestinian Liberation Organisation. The appellant accused Cosgrove of apparent bias on the ground that the judge was a founder member of the Scottish branch of the International Association of Jewish Lawyers and Jurists, whose newsletter had published articles supporting Israel.

The asylum seeker’s complaint was dismissed by the law lords in 2008 because Cosgrove had not associated herself with anything that had appeared in the newsletter. Expanding on his own opinion in the case, Hope comments that the result might well have been quite different if the judge had ‘dropped even the slightest hint on any occasion, however informal, that she was in sympathy with what was published’.

Hope ends his lecture with a call for judges to engage with the public when it is safe and proper to do so. Neuberger agrees that judges can help maintain judicial independence by giving lectures, though they may risk undermining independence if they cross the boundaries. To help fellow judges identify those boundaries, he offers a number of principles.

Judges have an important role to play in commenting on a wide range of issues, he says, but they should give careful consideration to the impact this may have on any cases they may have to decide.

They should consider the effect of their remarks on the judiciary as a whole. If they wish to disagree publicly with fellow judges, they should do so in a ‘seemly’ way. It would be very exceptional for a judge from England or Wales to express disagreement with the lord chief justice on a policy or constitutional issue.

Reticence is required before straying into areas for which the executive or the legislature is responsible, Neuberger believes. Judges should also consider how their comments will play in the media. They should not seek publicity for its own sake. And, while acknowledging that he might be a serial offender, Neuberger cautiously suggests that judges are giving too many speeches at the moment.

I don’t agree. But one solution may be not to tell anyone about them.