His remains are kept in Windsor Castle despite campaigns for their return.
Strands of Emperor Tewodros II’s hair were given to the National Army Museum in London 60 years ago.
The museum told the BBC it had decided not to make photographs of the hair public out of respect, because the matter was “too sensitive”. The remains are described as two pieces “no bigger than the size of a two-pence coin”.
The National Army Museum has now agreed to return the artefact, but says it is not returning any other items of African origin.
“It’s definitely not a precedent,” a spokesperson for the museum told the BBC.
“That’s the only one that’s been requested. They have to be formal, written requests to the director with a case”.
The BBC’s Emmanuel Igunza in Addis Ababa says talks about the process of repatriation with the Ethiopian government are set to begin within the next few days.
The move has reignited demands for the UK to return all the looted artefacts on display in British museums.