The offensive is Nato's largest-ever in the country.
But it will involve only half the number of soldiers that fought in a US offensive in the same region just nine months ago, when some 11,000 US-led troops attacked fighters in northern Helmand province during Operation Mountain Thrust.
"We cannot allow extremists, criminals and Taliban to decide what happens in this country," van Loon, said. "We need to make sure the government of Afghanistan with our support ... secures the area."
The government has little control over many parts of northern Helmand, and the British troops stationed there fight almost-daily battles with fighters.
"Strategically, our goal is to enable the Afghan government to begin the Kajaki project"
Ton van Loon, ISAF
US intelligence officials say Taliban fighters have flooded into Helmand over the last several months, and there are now more fighters there than any other part of the country.
The Taliban still control the town more than a month after the initial attack. Collins said forces would not move into the village until given approval by the government.
'Long term initiative'
British troops have also been battling militants in the nearby district of Kajaki to enable repair work on a hydroelectric damn there, which supplies close to two million Afghans with electricity, officials said.
"Strategically, our goal is to enable the Afghan government to begin the Kajaki project," van Loon said.
"This long-term initiative is a huge undertaking and the eventual rehabilitation of the Kajaki multipurpose dam and power house will improve the water supply for local communities, rehabilitate irrigation systems for farmlands and provide sufficient electrical power for residents, industries and commerce."
Separately on Tuesday, the Taliban said it had "arrested" a Briton working for an Italian newspaper.
The group said Danny Kell was a British military spy working for the Italian La Repubblica newspaper.
The paper and Italian foreign ministry said one of its correspondents, Daniele Mastrogiacomo, had not been in contact for two days.
British, Italian and Afghan authorities said they were investigating.