By Estelle Shirbon

LONDON (Reuters) - Britain's Supreme Court held the first secret session in its history on Thursday to consider evidence about an Iranian bank's alleged links to Tehran's nuclear program that the British government does not want to make public.

The court's decision to go into a so-called "closed hearing" to hear part of the government's case for imposing sanctions on Bank Mellat is contentious because it means the bank itself will not be shown all the evidence against it.

"This is a decision which is reached with great reluctance," the president of the Supreme Court, David Neuberger, said in a statement in open court just before Bank Mellat's lawyers, the media and the public were asked to leave for about 45 minutes.

"No judge can face with equanimity the prospect of a hearing, or any part of a hearing, which is not only in private, but involves one of the parties not being present or represented at the hearing," Neuberger said.

Civil rights campaign group Liberty, which had intervened in the case to try and stop the court from holding a secret hearing, said the decision of the judges was "a sad landmark in British legal history".

"The creep of secrecy has now reached our highest court, a body with a noble tradition for upholding justice and the rule of law," Liberty's legal officer Corinna Ferguson said in a statement.

The British government decided to impose sanctions on Bank Mellat in 2009, under the terms of the Counter-Terrorism Act, on the grounds that the bank had indirectly aided the Iranian government's nuclear program.

"UNHAPPY PROCEDURE"

Bank Mellat, Iran's biggest private sector lender, denies it helped the nuclear program in any way is appealing against the decision to impose sanctions. It won a separate legal battle to have EU sanctions against it lifted in a European court in January.

The problem for Britain's Supreme Court is that a lower court that considered the case in 2010 heard part of the government's evidence against Bank Mellat behind closed doors, and issued a judgment that was partly "closed", or secret.

The bank's lawyers have never had access to the closed part of the judgment and do not know what evidence the court was shown to reach that judgment.

The government's lawyers have argued that the Supreme Court, Britain's highest appeals court, should consider the closed part of the 2010 judgment so that it could have the full picture when deciding on Bank Mellat's appeal against the sanctions.

Neuberger said the Supreme Court judges were "very dubious indeed" about the government's arguments but had nevertheless decided to go ahead with "this unhappy procedure".

He said when it eventually gave its judgment on the appeal, the court would give as much detail as it could about what it had seen during the secret hearing to Bank Mellat and the public.

Bank Mellat's lawyer, Sarosh Zaiwalla, was not immediately available for comment.

In a previous statement about the case, before the secret hearing took place, he said: "The right for any individual to see the case against them and answer it directly is a fundamental principle."

(Editing by Andrew Heavens)