Latest reports from southern Afghanistan suggest that Sangin district in Helmand province is now almost entirely under Taliban control after days of fierce fighting.
The police headquarters and the main government building fell to the Taliban on Wednesday, a local senator said.
The Taliban say their fighters have seized the entire district.
However, the Afghan defence ministry said fighting was continuing and that reinforcements had been sent.
Sangin saw almost a quarter of British military fatalities during the UK's combat mission in Afghanistan.
District governor Haji Suliman Shah told the BBC he had been airlifted from the district HQ to Shorabak base - formerly Camp Bastion - in the provincial capital Lashkar Gah early on Wednesday, along with 15 wounded security force members.
A few hundred police and soldiers have taken refuge at an army barracks about 7km (four miles) from Sangin, and are besieged there.
Why Sangin matters
- Sangin is a rich production centre for opium in Helmand province
- Helmand is a major centre of the Taliban insurgency and borders Pakistan
- Of the 456 UK military deaths in Afghanistan from 2001 to 2015, almost a quarter were killed in and around Sangin
- US and British troops have been sent to Helmand in the last few days, but in an advisory role only
Ashuqullah, a police officer at the barracks, told the BBC the "entire" town was controlled by militants. "We have not seen any help," he said.
"Support troops have been airdropped at a distance... but all roads are blocked and in the militants' control," he added.
There were many wounded at the barracks needing urgent evacuation, he said.
Speaking in Kabul, Afghanistan's acting Defence Minister Masoum Stanikzai described the situation in Helmand as "manageable" and said fresh support troops had been sent in.
Afghan government forces had been "thinly spread" over the whole country, he said, and had been trying their best to hold all areas.
A small contingent of British troops has been sent to Helmand "in an advisory role," the British government said on Tuesday.
A Taliban spokesman, Qari Yousuf Ahmadi, claimed on Wednesday:
"The Sangin district centres, its police HQ, and other establishments were under continued attacks of the mujahideen and today... with God's grace the district was fully captured by the mujahideen.
"The white flag of the Islamic emirate is at full mast at the district now.''
Haji Daud, the head of the Sangin district people's council, told the BBC that Sangin residents had fled the district to neighbouring areas.
Responding to the defence minister's claims, he said: "Those whose family - brothers and siblings and parents - are not fighting on the front, they always say the situation is not dangerous in the area..."
"Those who make such comments do not care to defend Helmand."
Pharmacy owner Sarwah Shah, who fled to Lashkar Gah, told the BBC that all of the families living on his street in Sangin - around 20 to 30 houses - had fled.
Another resident Agha Wali said he had fled Sangin with his children two days ago. He had had to leave all his possessions behind, he said.
The Taliban have already seized control of all but two districts in Helmand.
On Monday the deputy governor of Helmand complained of a lack of government support in an open letter on Facebook to President Ashraf Ghani.
"Helmand will collapse to the enemies and it's not like Kunduz, where we could launch an operation from the airport to retake it. That is just impossible and a dream," he wrote.
In September, the Taliban briefly overran the northern Afghan city of Kunduz in one of their biggest victories since 2001.