The bitter legal battle over the government’s flagship immigration policy is set to reach new heights after Downing Street insisted it would fight to overturn a ruling that sending refugees to Rwanda was unlawful. Charities and others were jubilant on Thursday after judges at the court of appeal ruled in favour of campaign groups and 10 affected asylum seekers, while the opposition claimed the policy at heart of Rishi Sunak’s “Stop the Boats” pledge was now unravelling. But the prime minister was quick to announce plans to appeal at the supreme court against the decision as he insisted that Rwanda was a safe country for asylum seekers to have their claims processed – and said the court had agreed with this. The home secretary, Suella Braverman, went further by claiming in the aftermath of the ruling that the “system is rigged against the British people”. Officials within government are privately even more bullish about its next legal fight, which could pave the way for flights to take off before the general election. One No 10 source said: “The lawyers have spent all day poring over this and know exactly what they need to prove at the supreme court. They’ve got a good case to make”. The ruling follows a four-day hearing in April against last year’s high court decision that it was lawful to send some asylum seekers, including people arriving on small boats, to Rwanda to have their claims processed rather than dealing with their applications for sanctuary in the UK. The court of appeal subsequently ruled on Thursday that deficiencies in the Rwandan asylum system meant there was a real risk that people would be returned to home countries where they face persecution or other inhumane treatment, when in fact they had a good claim for asylum. Its conclusion was that Rwanda was not a “safe third country” even though assurances by the Rwandan government were provided in good faith. Government insiders, however, argued that Rwanda did not currently have returns agreements with any of the countries and that the UK had put safeguards in place when it signed a memorandum of understanding with Kigali. The illegal migration bill, now passing through parliament, states that all asylum seekers arriving by “irregular means” could face being forcibly removed to Rwanda. However, Labour claimed the government’s policy on so-called small boats crossing the Channel was now “completely unravelling”. The shadow home secretary, Yvette Cooper, told Braverman as she faced her in the House of Commons that the Rwanda scheme was “unworkable, unethical and extortionate”. During fraught exchanges in the Commons on immigration, which is set to be one of the dominant issues of the coming election campaign, Braverman claimed that it had been “a bad day for the British people”, adding: “Today is a good day for the people smugglers.” The SNP’s Patrick Grady asked her: “Isn’t this exactly what the government’s wanted all along? A fight with the judiciary, a fight with the House of Lords, triangulating the official opposition … doesn’t this play straight into their dog whistle agenda?” Sunak’s own backbenches implored him to reiterate his past hints of support for more draconian proposals promoted on the Tory right, such as withdrawing the UK from the European convention on human rights. An intervention by the European court of human rights was what halted the first attempt at sending a flight to Rwanda. The former cabinet minister, Simon Clarke, described the decision as “a deeply disappointing ruling in the face of the clear will of parliament”. He added: “We have to be able to control our borders. If the ECHR continues to forestall this, we have to revisit the question of our membership.” In their ruling, the judges said: “Nothing in this judgment should be construed as supporting or opposing any political view of the issues.” A summary was read out in the morning by the chief justice of England and Wales, Lord Burnett – who heard the appeal with Sir Geoffrey Vos and Lord Justice Underhill – who said the court had ruled by a majority that the policy of removing asylum seekers to Rwanda was unlawful, though he disagreed with the other two judges. The court heard from the UN’s refugee agency, the UNHCR, that Rwanda had a record of human rights abuses towards refugees within its borders, including expulsions, refoulement – forced removal to countries where they are at risk – and arbitrary detention. The agency said the Home Office would not be able to guarantee the safety of asylum seekers who were deported to the east African country. But Sir James Eadie KC, counsel for the home secretary, said Braverman was confident the government of Rwanda would abide by undertakings given in a memorandum of understanding signed by the two countries. Ten asylum seekers from Syria, Iraq, Iran, Vietnam, Sudan and Albania, who arrived by crossing the Channel in small boats, brought the case along with the charity Asylum Aid. The judges found that sending asylum seekers to Rwanda would be a breach of article 3 of the ECHR. The judges unanimously rejected other grounds of appeal in the case. There was a critical reaction from the government of Rwanda itself, which said through a spokesperson that it “took issue” with the ruling that Rwanda was not a safe country for asylum seekers and refugees. They added: “Rwanda remains fully committed to making this partnership work. The broken global migration system is failing to protect the vulnerable, and empowering criminal smuggling gangs at an immeasurable human cost. When the migrants do arrive, we will welcome them and provide them with the support they’ll need to build new lives in Rwanda.” Lawyers for the appellants and human rights campaigners welcomed the ruling. Toufique Hossain of Duncan Lewis solicitors, who represented some of the appellants, said: “The home secretary’s ‘dream’ and ‘obsession’ is in tatters. The court of appeal has ruled by a majority that Rwanda is not a safe third country. We speak on behalf of all our deeply vulnerable clients in thanking the court for its decision.”