Cpl Lee Scott was married with two young children
Defence Secretary Bob Ainsworth has rejected claims UK troops in Afghanistan are ill-equipped, saying more helicopters could not remove risk.
Opponents said up to 4,000 more troops - backed by helicopters to keep them away from roadside bombs - were needed, after 15 soldiers died in just 10 days.
Former defence secretary Lord King says the helicopter shortage is "critical".
In the first 10 days of this month, 15 members of the UK's armed forces were killed in Afghanistan.
Prime Minister Gordon Brown insists the mission is showing "signs of success".
He told the British Forces Broadcasting Service: "Despite the losses, our forces are doing a magnificent job."
UK troops have spent recent weeks on an offensive - codenamed Panther's Claw - which is designed to increase security ahead of Afghan elections, planned for next month.
It has coincided with a sharp increase in the number of British soldiers killed, with eight fatalities in the space of 24 hours between Thursday and Friday.
The six soldiers killed in Afghanistan on Friday have been named.
Father-of-two Lee Scott, 26, from Norfolk, a 2nd Royal Tank Regiment corporal was killed in an explosion near Nad Ali.
Five members of the County Down-based 2nd Battalion The Rifles died in two explosions near Sangin, Helmand on the same day.
They were: Cpl Jonathan Horne, and Riflemen Joseph Murphy, Daniel Simpson, William Aldridge and James Backhouse.
Those who died on Thursday have been named as Rifleman Daniel Hume, 22, of 4th Battalion The Rifles, and Private John Brackpool, 27, of Prince of Wales' Company, 1st Battalion Welsh Guards.
Much of the danger to British troops has been attributed to improvised roadside bombs.
Lord King said a lack of helicopters meant troops and supply vehicles spent more time on the roads.
American forces had eight times as many helicopters for the number of personnel, he claimed, adding that the UK "never had enough troops to do the job".
A former commander of British troops in Bosnia, Col Bob Stewart, claimed commanders in Afghanistan had repeatedly asked for up to 4,000 extra personnel.
"It's all very well going out on these operations. It's absolutely futile if you take the ground at considerable cost... then actually just withdraw because you haven't got the manpower to hold the ground."
However, the government maintains troop numbers are sufficient, having been boosted from 5,500 to 9,000 ahead of the current offensive and gained the backing of an extra 20,000 Americans.
In an interview with Sky News, Mr Ainsworth refused to be drawn on conflicting reports that troop levels would be further increased, or even cut, saying only that they would be kept "under review".
Ministers say 1,000 extra vehicles have been sent since last year and that new Ridgeback armoured vehicles and Merlin helicopters would also be provided by the end of 2009.
But Mr Ainsworth said extra equipment could not eliminate risk, pointing out that two recent victims were killed while getting out of one of the British Army's most heavily armoured vehicles - the Mastiff.
He also referred to the deaths of five soldiers from the 2nd Battalion The Rifles. They were on patrol when killed in two separate blasts, near Sangin.
Private John Brackpool was among the latest UK casualties in Afghanistan
"They can't do that from a helicopter and they can't do that from an armoured tank. Our people take risks every day and they want us to understand that," Mr Ainsworth added.
"They will tell you they have seen a massive improvement in personal kit and equipment, with vehicles as well."
Both Gordon Brown and Barack Obama have paid tribute to the soldiers killed in recent days, with the US President describing Britain's contribution as "critical" to the future stability of Afghanistan.
The prime minister said: "The operation in Helmand province is showing signs of success.
"Our troops are making progress as they attempt to make the area safer."
He said three quarters of terrorist plots dealt with by UK security services originated in the mountainous border area between Afghanistan and Pakistan.
This "chain of terror" justified Britain's continued military presence in Helmand, he said.
Stuart Trow, who became the first British casualty in Afghanistan when he lost his left leg in 2001, agreed with Mr Brown and said he still supported the mission.
He said: "You know at times my heart cries out and says: 'Wouldn't it be nice to get these guys back?'
"But the head rules on this one and what these guys are doing is essential to safeguard the security and safety of us and our children and grandchildren," he added.
Former Liberal Democrat leader Sir Menzies Campbell called on the prime minister to bring all parties together to agree a strategy for Afghanistan.
"Political uncertainties run the risk of affecting the morale of troops on the ground and their families at home," he said.
BRITISH CASUALTIES IN AFGHANISTAN MARCH 2006 - JULY 2009
1: Highest monthly toll with 19 dead including 12 killed when a RAF Nimrod crashes in Afghanistan.
2: British death toll reaches 100. Among the 13 fatalities in June is the first British female soldier.
3: British casualties surge as major offensive against Taliban begins in the south. Many are lost to powerful Improvised Explosive Devices.