The government is facing a legal challenge over the deployment of its armed drones as British officials come before a United Nations inquiry this week into the legality of targeted killings.

Amid claims the RAF's Reaper squadron could move from Afghanistan to operate against jihadists in the Middle East, Whitehall has been criticised for its reluctance to engage with the Geneva-based investigation.

The Ministry of Defence has repeatedly refused to state what it intends to do with the 10 Reapers – controlled remotely from RAF Waddington in Lincolnshire and a USAF base in Creech, Nevada – once UK operations in Afghanistan finish in December.

Lawyers working with the human rights group Reprieve have now signalled their intention to bring a judicial review challenge, on behalf of a Yemeni citizen, against the MoD if the government does not reveal where the drones will be flown outside Afghanistan and the UK.

The legal threat has emerged as British officials go before the UN's human rights council in Geneva on Monday. The inquiry was launched by Ben Emmerson QC, the UN's special rapporteur on counter-terrorism, to examine the legality of drone strikes.

A letter to Emmerson from Tom Watson MP, the former defence minister who is chair of the All Party Parliamentary Group (APPG) on drones, Lord Hannay, the former UK ambassador to the UN who is chair of the APPG on the UN, and Sir Jeremy Greenstock, the former diplomat who is chair of the UN Association in the UK, criticises the government's response.

The letter, seen by The Guardian, states: "We note that the [Human Rights Council] session has now commenced and the UK government does not appear to have responded to the special rapporteur."

Watson told The Guardian: "On the verge of another remote war in Iraq, we need UN guidance on how to apply international laws to armed drones more than ever. As chair of the APPG on drones, I am urging Emmerson to set this in motion. It's disappointing that the UK government have failed to implement [his] advice. This is not the end of the road."

Ahead of the Geneva meeting Emmerson said: "There is a pressing need for clarity, transparency and accountability about the use of armed drones in counter-terrorism operations, and the level of civilian casualties they inflict.

"This week's debate at the human rights council is a milestone in that process. It represents a serious attempt by the UN and international community to reach some agreement about the legal framework governing drone use.

"The resolution calling for this debate was sponsored by Pakistan, and passed by a majority of states on the council. But it was opposed by the United Kingdom and the United States. It was disappointing that two of the states who have made the greatest use of drones in counter-insurgency operations voted against holding a public debate at the Council."

"I very much hope that both states will now participate in the discussion and explain their legal justification for the use of armed drones. They need to engage in meaningful debate – to explain the rules of engagement that apply to the use of drones in counter-terrorism operations, and to be transparent about the number of civilians who have been killed or injured in these operations."

A Foreign Office spokesperson said: "The UK regards [Emmerson's] report as important, and shall be attending the human rights council panel discussion... We appreciate this opportunity for discussion and shall be making a statement at the meeting."

Reprieve's legal challenge is focused on Yemen because of past speculation that UK drones could be used against jihadi groups there. In July, the defence minister Mark Francois told MPs: "The UK intends to retain the Reaper capability primarily for its intelligence, surveillance and reconnaissance capabilities after combat operations in Afghanistan have ceased.

"As is the case for the routine deployment of other military assets, the MoD may notify parliament of the deployment of UK reaper RPAS but there is no intention for parliamentary approval to be sought prior to each deployment or re-deployment."

Reprieve's legal director, Kat Craig, said: "It is bad enough that the UK already supports the CIA's secret, illegal drone campaign but there is now a real risk that Britain will follow the US down the slippery slope to an endless, global war without limits and without accountability. The public must be allowed to know when and where our government sends armed drones to carry out deadly strikes – if the government resists this, it will strike at the heart of our democratic traditions."

Daniel Carey, a solicitor at the law firm Deighton Pierce Glynn which has served the letter before claim, said: "Using drones outside of armed conflict will be a step change in UK drone operations, yet the MoD is refusing to tell even parliament what its plans are. Our client [Saeed Al Yousefi] does not want to see the UK's drones in the skies of Yemen."