The Islamists broke through the frontlines of Sangin on Sunday after days of pitched clashes with besieged Afghan forces, tightening their grip on the southern province of Helmand.
Fleeing residents reported Taliban executions of captured soldiers as the insurgents advanced on the district centre, compounding fears that the entire province was on the brink of a security collapse.
Government officials today denied reports that Sangin was on the brink of falling to the Taliban, saying that reinforcements were trying to relieve dozens of security forces holed up in the district centre.
But Taliban spokesman Zabiullah Mujahid claimed insurgents had overrun the entire district, pinning down Afghan forces in a military base where trapped soldiers reported dire conditions.
"Our men are hungry and thirsty," Abdul Wahab, a local police commander in Sangin, told AFP.
"Stepping out to get bread means inviting death," he said, adding that dozens of his comrades had been killed and grievously wounded.
The war in Helmand, seen as the epicentre of the expanding insurgency, follows a string of military victories for the Taliban after NATO formally ended its combat operations last year.
The turmoil in Helmand, the deadliest province for British and US forces in Afghanistan over the past decade, underscores a rapidly unravelling security situation in Afghanistan.
Britain on Tuesday said a small contingent of its troops had arrived in Camp Shorabak, the largest British base in Afghanistan before it was handed over to Afghan forces last year.
The deployment, in addition to a recent arrival of US special forces in the region, is the first since British troops ended their combat mission in Helmand in October 2014.