He was the seventh British soldier to die in a week.
Lieutenant Colonel Nick Richardson, the spokesman for Task Force Helmand, said: "This soldier gave his life for the security of his own country and the freedom of the Afghan people; there is no greater sacrifice than this."
Britain has around 8,300 troops in Afghanistan, largely battling Taliban fighters in Helmand.
US marines launched the Helmand offensive with violence at its worst levels since the Taliban were ousted in 2001 for refusing to hand over al-Qaeda leaders behind the September 11 attacks on the United States.
Helmand is also the source of most of Afghanistan's opium crop, the world's largest, which finances the Taliban.
Gun battle
Elsewhere in Afghanistan, a gun battle in the eastern province of Nuristan has killed at least six police officers and 21 suspected Taliban fighters, a senior official said on Wednesday.
The fighting erupted on Tuesday when the fighters attacked government buildings in Nuristan's Barg Matal district.
Eight Afghan policemen were also seized by the Taliban fighters.
Jamaluddin Badar, the Nuristan governor, appealed for help as gun fight showed no signs of abating.
"The fighting is continuing right now and we urgently need reinforcements. Eight of our police have been captured," Badar said.
Lurking dangers
Increasing violence is making Afghanistan riskier for journalists.
Al Jazeera's Zeina Khodr narrated the dangers she faced while returning from a visit to Helmand.
"We drove 15km from Lashkar Gah, the provincial capital of Helmand, and we couldn't continue further because a bridge was destroyed by the Taliban. We had two options, either go back or use the dirt road, which means travelling through Taliban controlled villages.
"So we drove on for a few hundred metres and saw the Taliban setting up a checkpoint and we were stuck in the middle between a destroyed bridge and the checkpoint," she said.
"Then we saw the Taliban up in the hills surrounding the whole area, which they say was part of their operation in response to the US-led offensive against their strongholds in the south.
"While we were stuck, we made a number of phone calls both to the governor of Helmand and the police commander. They had promised to send a convoy of security service to help us leave the area, but it took them a long time because they had to advance slowly because the Taliban laid siege to the whole area," she said.
Kohdr said: "We couldn't wait long and we saw a convoy of civilian cars and decided to drive with them along a dirt road and after approximately five km, we saw the Afghan security convoy on their way to help us leave the area, so it shows you how the Taliban are really everywhere."