"We knew this summer was going to be tough fighting - we still have a long way to go."
Pte Brackpool, a father-of-one, would have been celebrating his 28th birthday on Saturday.
His platoon commander, Lieutenant Dave Harris, said: "He had a permanent smile etched across his face and appeared to relish being part of a close knit team despite the austere conditions.
"All of us in will remember Private Brackpool as a genuine, compassionate man who gave his life protecting his comrades."
Private Brackpool would have been celebrating his 28th birthday
He died from a gunshot wound during a battle against Taliban fighters in the Lashkar Gah area.
Rifleman Hume's parents Adrian and Wendy said in a statement: "Daniel passed out of Catterick as top recruit and since joining the Army he was the happiest we had known him.
"We have lost a son and a best friend. His death has left a huge void in our lives - we are fiercely proud of him."
Colleagues described him as "exceptionally gifted", while his family said the Berkshire-born soldier had found his place in the world since joining the Army.
The current major assault against the Taliban in Helmand aims to improve security ahead of next month's Afghan elections.
Many UK troops are fighting in the south under the auspices of Operation Panchai Palang or Panther's Claw.
Mr Brown, who will appear before the Commons Liaison Committee next week, told its members the Afghanistan-Pakistan border had emerged as "a new crucible of terrorism" linked to three-quarters of the most serious plots against the UK.
In the letter, he said: "So our purpose is clear: to prevent terrorism coming to the streets of Britain.
"Our security depends on strengthening the Pakistan and Afghan governments to defeat both al-Qaeda and also the Pakistan and Afghan Taliban."
Alistair Darling: "We've got to make sure our troops are properly equipped."
He added that if the Taliban were allowed to "overwhelm Pakistan's democracy", al-Qaeda would have "greater freedom from which to launch terrorist attacks across the world".
Mr Brown went on: "So this is a fight to clear terrorist networks from Afghanistan and Pakistan, to support the elected governments in both countries against the Taliban, to tackle the heroin trade which funds terrorism and the insurgency, and to build longer term stability."
He also paid tribute to "the fearless work of our troops" and added that despite the "tragic losses", morale remained high.
BBC correspondent Ian Pannell, who is embedded with British troops in Afghanistan, said the main threat came from improvised explosive devices (IEDs) hidden in the ground.
"Every morning when the troops leave their compound and go out on operation, they don't really know whether or not this will be their last operation - and that's the danger that they have to live with every day," he said.
The Stop the War coalition has announced a protest in London on Monday, calling for troops to be withdrawn from Afghanistan in light of the losses.
A group spokesman said: "The troop surge which was meant to pacify Helmand province has become a nightmare for the British army."
One hundred and eighty-four service personnel have died in Afghanistan since 2001, more than the 179 who were killed during the war in Iraq.
On Friday in Helmand, five soldiers from the 2nd Battalion The Rifles were killed in two separate blasts near Sangin, while a member of the 2nd Royal Tank Regiment died near Nad Ali.
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.
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