The Campaign Against Arms Trade (CAAT) says UK fighter jets and bombs sent to the Gulf state have been used in the conflict in Yemen in which thousands have died.
The group is attacking the Government's refusal to suspend existing sales licences for weapons or military equipment and to halt the granting of new licences.
The case is being seen as potentially having a wide impact on the arms trade generally, which could become even more important to the economy in post-Brexit Britain.
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CAAT says over 10,000 people have been killed as a Saudi Arabia-led coalition intervenes in the Yemeni civil war.
It says the fighting has created a humanitarian catastrophe, destroying vital infrastructure and leaving 80 per cent of the population in need of aid.
But the UK has continued to allow sales, with over £3.3 billion worth of arms having been licensed since the bombing began in March 2015.
Britain’s arms sales to Saudi Arabia are being challenge in the High Court
The Government are refusing to suspend existing sales licences for weapons or military equipment
CAAT spokesman Andrew Smith said: "For almost two years now, the UK has been complicit in the destruction of Yemen.
UK fighter jets and bombs have played a central role in the bombardment
CAAT spokesman Andrew Smith
"UK fighter jets and bombs have played a central role in the bombardment, and UK political support has helped to underpin and legitimise it.
"We are always being told that the UK stands for free speech and democracy, yet it has sold billions of pounds worth of arms to one of the most brutal and repressive regimes in the world to use against one of the poorest countries in the region."
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Rosa Curling from law firm Leigh Day, which is representing CAAT, said: "We believe that the decision taken to continue to grant new licences for the sale of arms to the Kingdom of Saudi Arabia is unlawful.
Yemen Crisis: 19-month civil war continues Wed, November 16, 2016
Schools and hospitals have been bombed, children are currently malnourished, the scale of suffering is the result of an ongoing conflict in Yemen. An estimated 10,000 people have been killed, according to the UN. Express Pictures reports the shocking photographs taken from inside the ongoing crisis in Yemen.
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Intensive care wards in Yemen's hospitals are filled with emaciated children hooked up to monitors and drips
The Campaign Against Arms Trade claim UK fighter jets and bombs are being used in the Yemen
"There is increasingly evidence being unearthed that the Saudi-led coalition has committed serious breaches of international humanitarian law in Yemen."
Martin Chamberlain QC, representing CAAT, had said when he recently applied for permission to seek judicial review that the UK had supplied weaponry which had, or was very likely to have been, used in air raids, and that schools and hospitals had been hit.
Mr Chamberlain said investigations by various international organisations, including the UN Security Council's panel of experts on Yemen, had concluded that the Saudi coalition was in serious breach of international human rights laws.
The case could have a far-reaching impact on the arms trade
He accused the Government of erring in law after concluding the threshold for suspending arms licences had not been triggered despite the breaches that had been established.
James Eadie QC, representing the Government, submitted that the CAAT case was unarguable as the Government had based its decision on "a body of information" not available to the UN and NGOs.
The full application for judicial review is being heard over three days by Lord Justice Burnett and Mr Justice Haddon-Cave sitting in London.
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