The UK government could face legal action after David Cameron revealed he ordered a British drone to target and kill Islamic State (Isis) fighters in Syria. The challenge comes after the prime minister dramatically told MPs that a pilotless RAF aircraft killed Reyaad Khan and Ruhul Amin in Raqqa on 21 August.

The Conservative leader told the House of Commons on 7 September that the strike against jihadists was an "act of self-defence" as Khan, who was previously based in Cardiff, had planned to attack high profile targets in the UK.

But the prime minister stressed the action was separate from any military intervention in Syria from Britain, which Cameron said he would still seek parliamentary approval for.

"If there is a direct threat to the British people and we are able to stop it by taking immediate action, then as prime minister, I will also be prepared to take that action," Cameron said. "We should be under no illusions – their intentions were the murder of British citizens."

But now Green grandees Caroline Lucas MP and Baroness Jenny Jones have teamed up with the charity Reprieve and law firm Leigh Day have now launched a campaign to question the UK government over its drone policy.

"The government appears to have adopted a 'Kill Policy' in secret – without parliamentary debate or the prospect of proper independent scrutiny. Sanctioning lethal drone attacks on British citizens is a significant departure from previous policy, as well as potentially unlawful, and it's deeply concerning that it has occurred without appropriate oversight," Lucas said.

"By refusing to publish the legal basis for these attacks, the government has created a legal and accountability vacuum. We need to be able to determine whether the attacks – and what they signify in terms of government policy – meet the robust conditions set out in international and domestic law.

She added: "I am part of bringing this case because if we want to be effective at countering terrorism then we must ensure we act lawfully. There are serious questions to be answered about the legality of the strikes, as well as the lack of robust oversight.

"Given the evidence from the USA, where former heads of defence and others have called their secret use of drones a 'failed strategy', it's crucial that the UK's actions to date and moving forward are subject to proper debate and scrutiny, particularly as its apparent new 'Kill Policy' goes beyond even what the US has been doing."