Meanwhile, Nato has announced that it is launching a new countrywide military operation with Afghan forces to keep pressure on the Taliban through the autumn and winter after the worst fighting in five years.
Elsewhere in Afghanistan, heavy fighting continued on Tuesday. A US-led multinational force air strike killed a suspected mid-level Taliban commander and up to 15 other fighters in southern Uruzgan province.
A Nato statement on the strike did not name the Taliban commander.
Afghan army forces battled fighters near the eastern border with Pakistan in a clash that killed 24 suspected fighters and a soldier, said the defence ministry spokesman, General Mohammed Zair Azimi.
It was not immediately possible to independently confirm the toll.
In Helmand's Garmser district, police killed four suspected Taliban and arrested six others, said Ghulam Muhiddin, the provincial governor's spokesman.
And in neighbouring Kandahar province, suspected Taliban destroyed an oil tanker transporting fuel for Nato-led forces and killed its driver, said a police official, General Abdul Raziq.
Mark Laity, a Nato spokesman in Kabul, said on Tuesday that the British troops withdrew from the Musa Qala district in Helmand province after tribal elders and the provincial governor agreed to take responsibility for security in the area.
He also said that the troops had left "because of the sustained period of calm" and added that Hamid Karzai, the Afghan president, had supported the move.
"There has not been any contact with the Taliban and they are not involved in this."
General David Richards, the British Nato commander in Afghanistan, said the British troops were redeployed because security had been established in Musa Qala.
"The word pulling out is wrong. We reserve the right to rebalance and move our troops in which ever way makes military sense," he said in Kabul.
Tribal chiefs and Afghan troops now controlled the district and Nato would send its forces back if needed, he said.
Musa Qala has been one of the most volatile regions of Helmand, where about 4,000 British troops who deployed to the province in the spring have been engaged in heavy fighting with the Taliban.
About 120 British soldiers were withdrawn from Musa Qala as part of the deal with local tribesmen.
No Taliban deal
Mohammad Daud, governor of Helmand province, said there had been no agreement with the Taliban.
He also rejected a reported statement by the Taliban that said the Afghan flag would no longer fly in the district.
"The Afghan flag is there, our new district chief, our new police chief with police are there," Daud said.
"There is not any kind of agreement [with the Taliban]. This was the demand of tribal elders."
Daud said the district leadership had also been changed, however, at the request of the tribal elders.
"They asked for good governors," he said.
In September, British Nato forces struck a deal with Musa Qala tribal elders in which the elders said they would drive out the Taliban in exchange for an end to military action that had caused heavy damage.
The deal resulted in a sharp drop in clashes, Nato said at the time.