A gay couple fighting against a Singapore law that criminalises sex between men has lost their bid for a Queen's Counsel to argue their appeal.

In a written judgment on Thursday, Justice V K Rajah dismissed the application by Mr Gary Lim and Mr Kenneth Chee for Lord Peter Goldsmith to present their case before the Court of Appeal.

Mr Lim and Mr Chee are challenging Section 377A of the Penal Code, arguing that it was unconstitutional. Their bid was dismissed by the High Court in April and they filed an appeal.

They also sought to have Lord Goldsmith, a former attorney-general in Britain who was involved in a fight against a similar law in Belize, Central America, to be allowed to present their case before the Court of Appeal.

In his judgment, Justice Rajah said the couple's application for Lord Goldsmith to be admitted has failed the requirements for Queen's Counsel to be admitted. The judge said he was not convinced that the issues in this case amounted to a "special reason" which would justify the admission of Lord Goldsmith.

Responding to the judgment, the couple said in a statement that they were disappointed.