The Defence Secretary has been urged to investigate after a soldier accused of killing a Kenyan woman was named by comrades.
The body of 21-year-old Agnes Wanjiru was found at the Lions Court Hotel in the town of Nanyuki two months after she disappeared in March 2012.
The town is close to the Batuk (British Army Training Unit Kenya) camp.
An initial inquiry was unsuccessful, but a fresh investigation has been launched after an inquest delayed until 2019 found Ms Wanjiru was unlawfully killed, the Sunday Times reported last month.
According to the newspaper, a soldier accused of the murder has been named by his comrades.
The soldier has allegedly confessed to the killing, and another soldier reported it to senior officers at the time - but no action was taken.
Former army chiefs call for an investigation
Former army chiefs have called on Defence Secretary Ben Wallace to look into the matter.
General Lord Richards of Herstmonceux, who was head of the armed forces when the murder happened, told the Sunday Times: “As far as an investigation is concerned, if in any doubt this allegation should most certainly be properly investigated.”
Former army head, General Lord Dannatt, said: “There are questions for the Ministry of Defence to answer.
“On the basis there is a strong allegation, this should be investigated, and it should have been investigated in the past.”
Labour's shadow defence secretary, John Healey, said: "Nine years on, justice must now be done for Agnes and her family.
"The Defence Secretary must take this more seriously. He should pledge the fullest co-operation to Kenyan detectives and launch an inquiry into any possible cover-up from commanding officers, military police or the MoD.
"When our forces serve overseas they stand up for British values and these allegations, if proven, would profoundly betray those values."
Jurisdiction with police in Kenya
An MoD spokesperson said: "In 2012, Special Investigation Branch carried out initial enquiries in Kenya, including providing information about British personnel to the Kenyan Police. No further requests were received at that time.
"Following the conclusion of a Kenyan inquest in 2019, we are aware that the Kenyan authorities are looking into this incident.
"The jurisdiction for this investigation rests with the Kenyan Police, and we are currently in discussions with the Kenyan authorities to determine what support is needed.
"Due to this being subject to an ongoing investigation it would be inappropriate to comment further."
On the death of Agnes Wanjiru in Kenya in 2012, a MOD spokesperson said: “The Defence Secretary is impatient with the pace of this and has directed full cooperation. He is working with the Military and Kenyan Police to ensure their investigation is not impeded.”