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It is understood that the British troops who died were travelling in a lightly armoured Land Rover, which is proof only against bullets and not mines. Commanders in Lashkar Gah say that the type of vehicle sent out on patrol is chosen according to the current assessment of the risk level.
So far 90 Nato personnel have been killed in Afghanistan this year.
The Prime Minister offered his deepest condolences to the bereaved families of the British casualties.
"They were in the most dangerous of jobs in the most difficult of circumstances," said Gordon Brown. "I salute not just their bravery, dedication and professionalism but that of all our armed forces. Our troops are the best in the world and fighting for the noblest of causes."
David Miliband, the Foreign Secretary, said British troops had to be present in Afghanistan because it was the only way that the job of stabilising the country could be done.
"We are in Afghanistan with a very clear mission to make sure that Afghanistan has its own institutions and its own security forces that ensure never again does it become a base for al-Qaeda. So we are there with a very clear national interest," Mr Miliband told Sky News.
"This is a joint political, economic and security drive, and that’s the only way this can be done. There needs to be reconstruction, whether it be schools or the hospitals or the economy, that allows Afghanistan to become a more normal country. It’s a very poor country but it doesn’t need to be a country overrun by al-Qaeda."
Lashkar Gar is the site of brigade headquarters for British troops in the area, and also a forward operating base in its own right, with regular patrols mounting sorties many times a day. The patrol that struck a mine is believed to have been a routine, planned operation that encountered disaster.
Taleban militants are increasingly using roadside mines and suicide bombers as tactics against Nato troops, mimicking Iraqi insurgents, after repeatedly being beaten back in direct military attacks and suffering the deaths of many of their leaders.
Brigadier General Carlos Branco, a spokesman for the Nato-led International Security Assistance Force in Afghanistan, said: "Our thoughts and sincere condolences are with the family and friends of the brave soldiers who were killed today. These soldiers died and were wounded trying to help bring peace and security for the Afghan people."
The Taleban claimed responsibility for the deaths. The Islamist group has been leading an insurgency since it was deposed from power by the US-led invasion in 2001.
"We blew up a Nato vehicle in Khokaba village near Lashkar Gah yesterday. Several soldiers were killed," said Yousuf Ahmadi, a Taleban spokesman.
News of the deaths came as Afghan and Canadian troops backed by helicopter gunships launched a major operation to drive Taleban militants out of villages in the Arghandab region, to the north west of Kandahar, where around 300 to 400 insurgents are said to be digging in after breaking fellow militants out of Kandahar jail on Saturday.
Nato spokesman Mark Laity said that the operation was going "satisfactorily", and clashes with the enemy had so far been minimal. The Afghan defence ministry says that 23 insurgents and two Afghan troops have been killed since the assault began at 8am.
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