The evacuation is being prepared as London fears that the Taliban could seize Kabul within a few days.
"We will not maintain a diplomatic presence. There is no trust the Taliban will honour any assurances,” the source told The Sunday Times.
UK Ambassador Sir Laurie Bristow will be evacuated by Monday evening, according to The Sunday Times.
The newspaper stressed that initially, the UK Foreign Office wanted to keep some of its officials, including Bristow, at the Kabul Airport, but those plans were revised due to the threat of the airport's seizure by the Taliban.
Afghanistan is seeing a spike in violence now as the Taliban have stepped up their offensive after international troops started a gradual withdrawal from the country, originally scheduled to be completed by September 11.
The pullout was stipulated in an agreement between the Taliban and the United States signed in Doha in February 2020.
*The Taliban is a terrorist group outlawed in Russia and many other countries