Fighter jets, bombs and missiles made in Britain are believed to have been used in the war, sparking a court battle over the legality of sales.
Research estimates that Saudi-led bombing has killed more than 8,000 civilians, while driving a deadly cholera outbreak and famine that the United Nations has called the worst humanitarian crisis in the world.
Government figures show that export licences worth £6.2bn have been granted to members of the Saudi-led coalition in the four years since the conflict began in March 2015.
The figure includes £5.3bn to Saudi Arabia, £657m to United Arab Emirates, £85m to Egypt, £72m to Bahrain, £40m to Kuwait and £142m to Qatar before it withdrew from the coalition in 2017.
The Campaign Against the Arms Trade (Caat) group said the real total was “likely to be a great deal higher” because many bombs and missiles used by Saudi forces were approved through a separate licensing system that offers no public breakdown.
Andrew Smith, of Caat, said: “Thousands of people have been killed in the Saudi-led bombardment of Yemen, but that has done nothing to deter the arms dealers.
“The bombing has created the worst humanitarian crisis in the world, and it wouldn’t have been possible without the complicity and support of Downing Street. These arms sales are immoral and illegal.”
Saudi Arabia leads a coalition conducting airstrikes in support of president Abdrabbuh Mansour Hadi in Yemen, and the British government has supported the intervention as a means of “fighting to restore Yemen’s legitimate government”.
In June, Court of Appeal judges found that the UK’s decision to continue selling arms to Saudi Arabia for use in the war was “irrational and therefore unlawful”.
A ruling said it “made no concluded assessments of whether the Saudi-led coalition had committed violations of international humanitarian law in the past, during the Yemen conflict, and made no attempt to do so”.
Judges found that although the UK had “engaged closely” with Riyadh in an attempt to minimise civilian casualties in Yemen, the efforts fell short of the legal obligation to assess the risk of war crimes.
In the wake of the ruling, former international trade secretary Liam Fox said the government would not grant any new export licences for weapons that may be used in Yemen.
But while seeking to appeal, the government is attempting to stay the Court of Appeal ruling and continue sales under pre-existing agreements.
Last month, it was revealed that the government had invited a Saudi delegation to the controversial Defence and Security Equipment International (DSEI) arms fair.
Protests are expected to greet DSEI when it arrives at London’s Excel Centre in September, with organisers boasting of its “unrivalled scale”.
The United Arab Emirates, which is part of the Saudi-led coalition in Yemen, is listed as an “international partner” on DSEI’s official website.
It says the state-owned Saudi Arabian Military Industries firm will also be among exhibitors.
Mr Smith called the invite “disgraceful”, adding: “This only goes to show that no matter how dire the humanitarian crisis in Yemen has become, the government will continue to prioritise arms sales over the rights and lives of Yemeni people.”
The government said it disagreed with the Court of Appeal’s judgment and has submitted a challenge to the Supreme Court.
A spokesperson said: “The UK operates one of the most robust export control regimes in the world. Licensing decisions are based on the most up-to-date information and analysis available at the time, including advice from those with diplomatic and military expertise and reports from our overseas network and NGOs.
“We welcome any further information NGOs can provide regarding compliance with international humanitarian law.
“The government undertakes a stringent process of scrutiny and approval before issuing any formal invitations to foreign governments to attend a major UK defence exhibition like DSEI.”
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