Peter Reynolds, 79 and his wife Barbie, 75, ran educational training projects in the country.
They were returning home when they were detained earlier this month. It is not clear why they have been arrested.
The couple’s four children wrote a letter to the Taliban urging for their parents’ release.
They wrote: “We do not understand the reasons behind their arrest.
“They have communicated their trust in you, and that as Afghan citizens they will be treated well.”
The couple were married in Kabul in 1970 and have been living and working in Afghanistan for almost two decades, staying after the Taliban took over in 2021.
“They became official Afghan citizens and have been living there for the past 18 years.
“Throughout this time, they have always been open about their presence and their work, diligently respecting and obeying the laws as they change.”
“Our parents have consistently expressed their commitment to Afghanistan, stating that they would rather sacrifice their lives than become part of ransom negotiations or be traded,” they added.
It is understood the couple’s family did not want the UK government to get involved with the case.
