It has been described as the forgotten war. One hundred thousand British soldiers fought in the Korean conflict between 1950 and 1953, but its hold on the memory of the nation is weak, a painful reality for the relatives of the 336 Britons still listed as missing in action and for whom there is no known grave.

But in an office located at Gloucestershire’s Imjin army barracks, named after the battle of Imjin River at which 650 soldiers of the Gloucestershire regiment faced 10,000 Chinese soldiers, the Ministry of Defence’s “war detectives” believe they may now be able to help keep some memories alive, thanks, in part, to Donald Trump.

When the US president met Kim Jong-un in Singapore in June, the North Korean dictator had pledged as a sign of goodwill to hand over remains of the allied dead from the Korean war, an act that duly took place later in the summer.

Caskets holding some 55 to 60 skeletons were given to the Americans, who are seeking to extract DNA from the remains in an attempt to link them to the missing.

Of the western allies that joined the US and South Koreans, the British suffered the second-largest losses in the war, an early cold war conflict. Researchers in the British Joint Casualty and Compassionate Centre (JCCC), who work on retrieving and identifying the British war dead, believe there is a chance that some of those remains will be theirs.

The task set for Nicola Nash, an archaeologist in the JCCC, known within the British army as the war detectives, is to trace the relatives of the British missing and secure a DNA sample to cross-check with the Americans.

Nicola Nash (left) at a burial ceremony for an unknown British first world war soldier near Ypres in Belgium. Photograph: David Levene/The Guardian

“The Americans are extracting DNA samples from the sets of remains that they were given and now all the nations that lost men during the Korean war are doing their best to get DNA samples from family members of men who died,” Nash said. “I have put together a definitive list of men with no known graves in the British armed forces during the war. There are around 300 but around 50 of those were lost at sea or buried at sea, so we have discounted those. All these remains have been found on land. So that leaves me with 255 families that I am trying to trace.”

The JCCC is trying to build family trees of the missing in order to get in contact with relatives. Of the 250 soldiers, the relatives of around 30 are in contact with them, with work on tracking the rest continuing.

“But all it takes is one family to read this and think, Oh, yeah, and make contact and that saves hours of work,” said Nash. “So once they get in contact with me I have a database to keep the information together. I have got DNA tests waiting to go out to families. Simple mouth swabs, all very easy, and we send that to them with a stamped addressed envelope, and they send it back to us and it goes over to the American lab.”

The work is familiar to Nash. Six months before Kim Jong-un handed over the remains found in North Korea, two skeletons were given to the British by the South Koreans.

Found by the Imjin River, both sides agreed that they were likely to be members of the “Glorious Glocs”, the Gloucestershire regiment that fought in the battle there in April 1951, from which only 40 of the 650 British soldiers escaped without being killed, wounded or captured.

Nash has DNA samples from those two sets of remains, and 20 DNA sets have been sent to the relatives of the Gloucestershire regiment soldiers who have no known grave, out of a total missing in action of between 35 and 40.

“Most of the relatives we have been in contact with are really close, you know, children, siblings,” said Nash. “So it is quite emotional for the families to have us get in contact after all these years.

“It is a small chance, but it is a chance that their relatives could be found,” she added. “I spoke to one chap who is the son of someone who died in the Gloucestershire regiment and it was really emotional for him. He had spent his whole life not knowing what happened to his father.

“The most important thing we want people to take away from this is if they have a relative with no known grave from the Korean war to get in contact with us,” Nash said. “The Americans lost by far the most but the next largest was the British, so there is every chance we will come across a positive match and, at that point, they would get the full military burial with honours at the UN cemetery in Busan.”