A former counter-terrorism minister, who was also head of the Royal Navy, has joined calls for the British government to publish its rules on intelligence sharing, that could lead to drone strikes beyond traditional battlefields, saying the current situation leaves UK personnel on “hazy ground”.

Admiral Lord West, a former first sea lord who served as a Home Office minister in the Gordon Brown Labour government, said intelligence sharing with allies such as the US was “crucially important” for protecting the country from national security threats.

But he said this protection should not be extended to “information about people we know are bad guys”, in situations where it could be used for extrajudicial killings. Campaign groups and a senior academic echoed West’s call for the government to be more transparent about its rules for sharing intelligence.

On Wednesday, the Guardian revealed documents provided by NSA whistleblower Edward Snowden that raised questions over potential GCHQ involvement in US drone strikes in Yemen and Pakistan, which are not recognised war zones. The government refused to comment.

West said: “What the US does is up to the US, but as far as our nation goes, I would not be happy if our country was carrying out killings in countries where we are not at war. Therefore I think it’s appropriate to disclose the guidance.”

During his time as a minister, West said there were times when reports of US counter-terrorism actions leading to the deaths of alleged terrorists made him feel “rather relieved”. But, he added, “You mustn’t let that cloud your judgment on what’s right and what’s proper.”

West said: “You sit at your desk and think, thank goodness that horrible man’s dead, [but] that doesn’t mean that’s correct. We have got to be seen to be whiter than white – because the people we are fighting against are so appalling.”

Prof Nicholas Wheeler, director of the institute for conflict, cooperation and security at the University of Birmingham, and the academic lead on a major report on the impact of drones, said the Snowden documents highlighted a continuing need to ensure that vital intelligence sharing “does not lead to the UK government and its intelligence officers inadvertently colluding in US drone attacks that, in the words of our 2014 report, ‘could be held to be contrary to international law’”. He added: “It is important that there is firm legal guidance in place on this issue”.

The Snowden documents included memos for GCHQ staff working on Overhead, a joint US, UK and Australian surveillance initiative, that includes staff based at Menwith Hill in Yorkshire. These included a reference to Overhead supporting a March 2012 drone strike in Yemen, which described how two alleged members of al-Qaida in the Arabian Peninsula were killed.

Further documents included legal guidance for officers in Afghanistan, and a 2009 document outlining surveillance priorities for the coming years. These were reviewed by leading barrister Jemima Stratford QC, who said they “raise questions about the extent to which UK officials may have had knowledge of, or helped to facilitate, certain US drone strikes which were not carried out in the context of an international armed conflict”.

Campaigners on both sides of the Atlantic have echoed the call for increased transparency. Hina Shamsi, a lawyer at the American Civil Liberties Union, which has conducted numerous legal cases aiming to expose details of the US covert drone wars, said: “These revelations underscore how little citizens of other democracies – the United States’ allies – know about their intelligence agencies’ activities, and cooperation with the United States, in a deeply controversial, and in some instances unlawful, killing programme.”

The UK has consistently refused to confirm or deny whether it does share such intelligence, although ministerial statements to parliament have strongly implied that it is not involved in strikes beyond legal battlefields. Last year, defence minister Mark Francois told parliament that “strikes against terrorist targets in Yemen are a matter for the Yemeni and US governments”.

An US Predator drone flies over Kandahar airfield, Afghanistan. Photograph: Kirsty Wigglesworth/AP

In 2012, the legal charity Reprieve helped a Pakistani tribesman, Noor Khan, launch a court case alleging that GCHQ may have contributed intelligence that led to the drone strike in which his father and almost 40 other civilians died.

Reprieve’s Jennifer Gibson said: “The British government has consistently said this is a matter for the countries involved. There is now damning evidence they are one of those countries. Both the US and the UK need to come clean about who they’re killing and why.”

She pointed out the discrepancy between GCHQ’s account of the Yemen drone strike, which reported two alleged militants killed, and reports of a strike that same day by the NGO AlKarama, which said a named civilian had been killed, and between six and nine children were wounded. It is not clear whether the two reports refer to the same strike, and GCHQ declined to comment.

Gibson said: “These latest revelations add even more weight to a glaring truth: the Obama administration has no idea who its drone programme is killing. UK cables say it killed only two men, while independent investigations on the ground show that up to nine were injured and killed, including children. How many others like them have also been killed? And crucially, what role did the UK play?”

Even before the Guardian’s report, senior figures in the security community had called for the rules to be disclosed. Last year, former GCHQ director Sir David Omand joined Prof Michael Clarke – chairman of the influential military thinktank the Royal United Services Institute – and MPs Tom Watson and David Davis, signing a letter calling on the Foreign Office to publish guidance “applicable to the passing of intelligence relating to individuals who are at risk of targeted lethal strikes outside traditional battlefields”.

The government would not comment on the specific points in the Snowden documents but a spokesman said: “It is the longstanding policy of successive UK governments not to comment on intelligence operations.

“We expect all states concerned to act in accordance with international law and take all feasible precautions to avoid civilian casualties when conducting any form of military or counter-terrorist operations.”