Two judges of the Court of Appeal granted permission for the plea on Friday, according to the Campaign Against Arms Trade (CAAT).
The campaign group challenged a High Court decision last July that found the granting of licences for arms exports from Britain to Saudi Arabia lawful.
CAAT took its case to the Court of Appeal, which said the case will be heard in the months ahead.
CAAT warned that British-made fighter jets, bombs and other munitions were being used by a Saudi-led military coalition that intervened in Yemen’s conflict in 2015, leading to widespread destruction in the country.
Andrew Smith, a spokesperson of CAAT, said the group was confident of winning the appeal.
“The Saudi-led bombardment of Yemen has killed thousands of people and created one of the worst humanitarian disasters in the world,” he said in a statement.
“Despite this, the Saudi regime has been armed and supported every step of the way by successive UK governments. We believe that these arms sales are immoral, and are confident that the Court of Appeal will agree that they are unlawful,” Smith said.
More than 10,000 people have been killed in Yemen since Saudi Arabia’s alliance launched its campaign to restore the internationally recognised Yemeni government.
It has carried out thousands of air raids against the Iran-allied Houthi movement that controls much of north Yemen including the capital, Sanaa.
Errant air raids have killed hundreds of civilians at hospitals, schools and markets.
The coalition denied targeting civilians in its campaign.
Britain’s Department for International Trade said it will defend the High Court decision.
“We remain confident that the UK operates one of the most robust export control regimes in the world and will continue to defend the decisions being challenged,” a spokesman told the Reuters news agency.
“We keep our defence exports under careful review to ensure they meet the rigorous standards of the Consolidated EU and National Arms Export Licensing Criteria.”