The two retired judges were sworn in last week as judges of the DIFC Courts, which administer a “unique common law, English language jurisdiction, which governs commercial and civil disputes, national, regionally, and worldwide”.

On Sunday, Mr Justice Clarke said he had resigned from the position after concerns were raised of there being a conflict of interest with his recent appointment as president of Ireland’s Law Reform Commission (LRC).

He said: “Ireland and many Irish companies do significant business in and with Dubai, and in that context it is important that there be an independent and trusted dispute resolution system available to those enterprises.

“However, I am concerned that the current controversy could impact on the important work of the Law Reform Commission, to which I am committed. In those circumstances, I can confirm that I have today submitted my resignation as a judge of the DIFC courts to the Chief Justice of that court.”

Professor Donncha O’Connell, an established professor of law at NUI Galway, acknowledged in a LinkedIn post that Mr Justice Kelly “has no such obvious conflict” but called on him to resign as well.

“Retired Irish judges should simply not be lending credibility to one part of the judicial system of a highly oppressive regime to create the impression (for business!) that there’s something approximating to the rule of law in that regime,” he wrote.

“The Judicial Council should proactively develop rules for retired Irish judges that are mindful of the need to protect the rule of law globally, not just in this part of the island of Ireland. In the meantime, Judge Kelly should do the decent thing, limit the damage already done and resign.”