A couple this week had their divorce settlement under Beth Din, or Jewish law, referred to by the High Court.
According to the Times, it is the first time in British legal history that an English family judge has agreed to refer a divorce dispute to a religious court.
The Muslim Council of Britain welcomed the judgement, which could pave the way for other couples to seek a divorce in a religious court, the Times said.
"If it leads to the eventual acceptance of Sharia court divorces, then Muslims will be very encouraged," a spokesperson said.
The case involved a couple of orthodox Jews in their 20s who married in 2006 in a Jewish ceremony and initially lived in Israel, returning to London for the birth of their first child.
They had planned to move to Toronto but the marriage began to break down and they separated in 2009, shortly after the birth of their second child.
Disputes over access to the children followed but before the case came to court in London, the couple decided to refer their disputes to a senior rabbi in the New York Beth Din and asked if the judge would agree.
Justice Baker was persuaded by the couple's arguments that arbitration in their own religious court would be better than litigation, and in line with their beliefs.
The judge said he examined the principles used by the Beth Din and ensured that they were in line with the laws in England and Wales.
He, however, did make it clear that the arbitration or ruling by the Beth Din was not binding.
The Beth Din published its full ruling on the couple's case in 2011 but further negotiations meant that a final settlement was reached only last year, and the judgement released by the High Court here this week.
Sharia has been operating in the UK, managed by locally-appointed councils, in parallel to the British legal system since 1982.
Thousands of Muslims turn to them to help resolve family, financial and commercial problems in accordance with Sharia principles.
However, these informal councils have no legal powers and they cannot impose any penalties. This could change in the wake of the latest High Court judgement.
