An Irish Christian bakery that was fined for refusing to bake a cake with engraved message supporting gay marriage has decided to appeal their case in the UK Supreme Court and European Court of Human Rights (ECHR) in Strasbourg.

A county court had initially ruled that they had discriminated against their customer in 2014 by declining a request to bake a cake with a picture of Sesame Street's Bert and Ernie along with a message 'Support Gay Marriage' and a logo of gay rights group QueerSpace. They were fined £500 in 2015 by the court.

The owners of Ashers Baking Co. challenged the decision in Northern Ireland's Court of Appeals which upheld the lower court's decision.

Now the bakers want to take the case to UK's highest court, but according to their lawyers they may be barred from doing so. If they are not able to appeal to the Supreme Court in London, they will try to further their case in European Court of Human Rights (ECHR) in Strasbourg. The matter will reach ECHR only on the condition that it is refused by the Supreme Court of UK.

"Under the complex rules regarding appeals in civil cases, such as the Ashers case, the Court of Appeal decision seems to be final, according to the terms of the Judicature Act 1978," said Simon Calvert, spokesman for the Christian Institute who are supporting Ashers. But he added that because of the broad public implications of the case, their lawyers have urged the Court of Appeals to decide if the appeal could be sent to the Supreme Court.

"In view of the complexity of these issues, however, and the wider public importance which this case clearly has, and in order to make clear that the appellants (Ashers) have exhausted their domestic remedies... we respectfully invite the Court of Appeal to consider giving a short ruling on the question of whether appeal to the UK Supreme Court is available in this case," said the letter written by Ashers' lawyers cited in Belfast Telegraph.

Ashers have six branches with over 80 employees, and deliver cakes across the UK and Ireland.