The McArthur family, who run the Ashers Bakery Company in Northern Ireland, were refused leave to appeal by the Court of Appeal in Belfast, however, they can now directly approach the Supreme Court in London.
A spokesman for The Christian Institute, which has been supporting the McArthurs, said: "Ashers Baking Company will take the necessary legal steps to instigate a Supreme Court appeal on this crucially important matter as soon as possible."
A case was made against Ashers after they declined the cake order in May 2014 on the grounds it went against their religious beliefs.
The Court of Appeal in Belfast upheld a ruling that the McArthur had discrimination against activist Gareth Lee in October this year.
Meanwhile, it's understood the Equality Commission in Northern Ireland (ECNI), which has been supporting Gareth Lee, had been hoping to retrieve up to £100,000 in costs from Ashers.
Judges at the Court of Appeal in Belfast have decided to limit the amount of the ECNI can retrieve from Ashers for the legal battle to date "dramatically", according to The Christian Institute.
The group's spokesman went on to say: "On the matter of costs the Court of Appeal judges have seen fit to limit the ECNI's recovery of their costs from Ashers to the same scale as the county court, a sliding scale which keeps costs proportionate to the value of the £36.50 cake and the £500 damages.
"This will have the effect of dramatically limiting the amount of legal costs which the ECNI can recover.
"The ECNI will be responsible for paying the vast majority of their expensive legal bills."