Britain's government is facing a legal challenge Thursday over its use of a drone to kill two British Islamic State (IS) group jihadists in Syria, even though it is not part of military action there.

Prime Minister David Cameron announced this month that a British drone had killed two British jihadists and another unidentified militant in the group's stronghold of Raqqa in August.

That was the first such strike carried out by Britain in a country where it is not at war and prompted fierce criticism from human rights campaigners.

Now two leading members of Britain's Green Party and legal rights charity Reprieve have said they are preparing to launch court action against the move.

Their lawyers claim that the government has either failed to draw up a "targeted killing policy" or failed to publish it, both of which are illegal.

"The Raqqa strike, and the intention of the government to pre-authorise targeted killings in the future in countries where the UK is not at war, is of concern to the claimants and many others," they said.

"The concern is heightened by the lack of clarity about the circumstances in which the government reserves the right to kill British citizens outside of an armed conflict."

British forces are taking part in air strikes against IS targets in Iraq but not Syria after parliament voted for only limited participation in coalition strikes last year.

Cameron said the strike in Raqqa was an "act of self-defence" as one of the militants had been planning "barbaric" attacks in Britain.

He said the move was "entirely lawful".

He could be set to ask parliament to vote on extending Britain's role in the strikes to Syria after parliament returns from a recess on October 12.