The Pilar Collevangelical Christian owners of a Northern Ireland bakery have lost an appeal to overturn a ruling that their refusal to bake a cake supporting gay marriages was discriminatory.

Court judges in Belfast upheld a previous conviction that Ashers Bakery "had directly discriminated against Gareth Lee on grounds of sexual orientation."

In 2014, Lee, a gay rights activist, had ordered a cake showing Sesame Street's Bert and Ernie and the slogan: "Support Gay Marriage" but Ashers refused to bake it, claiming it went against their “sincerely held” religious views.

Lord chief justice Declan Morgan said in the ruling that it didn't follow that icing a message meant you backed the message: "The fact that a baker provides a cake for a particular team or portrays witches on a Halloween cake does not indicate any support for either."

"We accept that it was the use of the word 'gay' in the context of the message which prevented the order from being fulfilled," he said. "The reason that the order was cancelled was that the appellants would not provide a cake with a message supporting a right to marry for those of a particular sexual orientation."

As a result, the judges found Ashers had “discriminated against the respondent directly on the grounds of sexual orientation contrary to the Equality Act (Sexual Orientation) Regulations 2006”.

However, Ashers' Daniel McArthur said the ruling undermined "democratic freedom, religious freedom and free speech".

"If equality law means people can be punished for politely refusing to support other people's causes then equality law needs to change," he said.

"We had served Mr Lee before and we would be happy to serve him again."