The UUP has said its two MPs will vote to trigger Article 50 to begin negotiations to leave the EU following the High Court ruling the matter must be put to parliament.
On Thursday, campaigners celebrated victory in the legal battle against Theresa May's decision to use the royal prerogative in her Brexit strategy, with demands for her to now set out her negotiating strategy to MPs.
However, the UK Government is to appeal the ruling.
In response the UUP, which campaigned to remain in the EU ahead of the June referendum, said: "We will study the detail of this judgement. We are very aware that the Government will appeal this decision in the Supreme Court and we will wait for the outcome of that.
"Parliament voted to give the people of the United Kingdom the opportunity to vote in a straight in/out referendum.
"On the June 23 the people of the United Kingdom voted to leave the European Union and on that basis, should the appeal be unsuccessful, our MPs will vote to trigger Article 50.”
The party has two MPs; Danny Kinahan represents South Antrim while Tom Elliott is the member of Parliament for Fermanagh and South Tyrone.
Meanwhile, the SDLP welcomed the ruling.
SDLP Foyle MP and member of the Westminster Brexit Committee Mark Durkan called on MPs from across Northern Ireland to "commit to representing the democratically stated will of people in Northern Ireland to remain in the European Union".
He said: “I welcome this important ruling by the High Court.
“I have consistently called on the government not to begin the formal process of triggering Article 50 on withdrawal from the EU until its proposals have been fully considered in the House of Commons and voted upon by MPs.
“Parliament has the right and the duty to ensure that we best consider how these matters are dealt with. However, the idea seemed to be that Parliament had no role whatsoever, and could entrust these matters entirely to the royal prerogative and those who are meant to be leading the process.
"That would constitute a request for us to commit a dereliction of duty.
“The SDLP has been consistent in its objection to the use and abuse of the dubious royal prerogative powers. Those of us who believe in parliamentary democracy know that major decisions where substantive details and strategic options count, should be debated and voted upon by MPs, rather than being pocketed as a private or personal tactic for a Prime Minister.
"SDLP MPs will unapologetically defend the will of the 56% of people who voted to remain in the European Union and the will of our constituents. It is now incumbent on other MPs from Northern Ireland to commit to representing the democratically stated will of people here."