Christopher Parry, 28, was with New Zealand aid worker Andrew Bagshaw when he was killed in the Soledar region of Ukraine a year ago.
They had been evacuating civilians from the Ukraine conflict.
Post mortem reports that Parry and Andrew Bagshaw were both killed by gunshot wounds to the head and other parts of the body - rather than the initial official explanation of their death, which was that their vehicle was hit by artillery fire.
Coroner Darren Salter, at the Oxfordshire's Coroners Court, cited some evidence that the Wagner group - a Russian-state funded private military company - was involved in the killing.
"The next step is getting it recognised as a war crime," Bagshaw told Morning Report.
"The important thing now is that we need to get actual evidence."
Dame Sue said the Parry family felt the same way.
Bagshaw said that the UK and New Zealand governments needed to send a investigator to Ukraine so they could investigate the deaths further.
"We know of an investigator in Ukraine who's got 10,000 cases on his desk and he cannot spend time on this particular event but if the UK and New Zealand got together, sent an investigator there, we could even direct them as to who they need to speak to, to get the evidence."
The parents said they had spoken to New Zealand's Ministry of Foreign Affairs and Trade and the UK's Foreign and Commonwealth Office.
Bagshaw wrote as recently as the 6 January to the Foreign Minister but has only got a computerised, automated response so far.
"At the time of their disappearance the New Zealand government basically abrogated their responsibility and just said we'll leave it up to the UK government to do something about it," said Dame Sue.
