"I can see serious difficulties with the idea that a witness should have her head covered where evidence is contested. If there is any question of credibility, it should be uncovered," Lord Neuberger, the president of Britain's Supreme Court, told 'The Times'.
"The jury system works in this country by contested evidence being decided by witnesses giving evidence before a jury and having credibility weighed - and one factor taken into account is the impression the witness makes and that includes being able to see the witness's face," he said.
"What I was saying that - and I don't think many would disagree - was that witnesses and parties in court may have beliefs, convictions, which are not those that most people have or the judge is familiar with and the judge should be sympathetic and understanding of those factors, such as a woman not used to appearing with her face uncovered."
He said that judicial policy on veil-wearing was decided on a case-by-case basis and that seemed to be working.
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"If the case-by case system breaks down I would be happy to have a general policy. But if it is not necessary, don't have it," he added.
On the UK government's review of Sharia courts, which is expected to begin in the coming weeks, Lord Neuberger said "given the concerns that undoubtedly seem to exist, it seems right to have an investigation and a review."
His comments come days after UK schools inspector Sir Michael Wilshaw warned that schools in the country are likely to be marked down if veil-wearing pupils or teachers were seen to impede communication and learning.