British soldiers near Nahr-e Saraj, close to where the explosion occurred. Photograph: Bay Ismoyo/AFP/Getty Images
The Ministry of Defence said on Wednesday the men had been killed on Tuesday in the Nahr-e Saraj district of Helmand province, on the border of Kandahar just north of the provincial capital Lashkar Gah.
It is understood six other Britons were injured in the explosion, which happened while the soldiers were inside a Mastiff troop carrier â€“ a 15-tonne vehicle which is regarded as one of the safest operated by the British military.
David Cameron said Britain had paid a “very high price” for the work it was doing in Afghanistan as he paid tribute to the three soldiers.
The soldiers who died were from the Royal Highland Fusiliers 2nd Battalion, Royal Regiment of Scotland, and can only have been in the country for a few weeks.
The MoD said the injured men received immediate medical attention and were evacuated by air to the military hospital at Camp Bastion but three could not be saved. Next of kin have been informed. The other soldiers hurt are not thought to have life-threatening injures.
The Mastiff is one of a number of fortified vehicles used by the British in Afghanistan that have helped to reduce the number of troops killed and injured by roadside improvised explosive devices.
Investigators will try to establish when the IED was planted â€“ some incidents have involved devices planted years ago. This roadside bomb must have been on a huge scale to have caused such damage, officials noted.
Though the UK has handed over lead responsibility for fighting the Taliban to the Afghan National Security Forces, British troops are still providing support to the local army and police, often in mentoring and support roles.
Major Richard Morgan, spokesman for Task Force Helmand, said: “It is with deep sadness that I must confirm that three soldiers from The Royal Highland Fusiliers, 2nd Battalion The Royal Regiment of Scotland, have died after their vehicle was struck by an improvised explosive device in the Nahr-e Saraj district of Helmand province.
“Our thoughts and prayers are extended to their family and friends at this difficult time.”
A MoD spokesman said the incident underlined the continued danger faced by soldiers as they prepare to pull out of Afghanistan in 2014.
“Our thoughts are with the families who have lost loved ones in this incident, which underlines the threats faced by our personnel as they continue to hand over security operations to their Afghan counterparts ahead of UK combat operations concluding by the end of next year,” he said.
“Security in Helmand, where most UK forces are based, is steadily improving with Afghan forces already responsible for the bulk of the province â€“ but the environment in which our troops operate remains risky and dangerous, including the threat of improvised explosive devices and insurgent attack.
“We will continue to do all we can to minimise these risks but they can never be removed entirely.”
The deaths take the number of UK service members who have lost their lives since operations in Afghanistan began in 2001 to 444. Six have died this year.
Officials first reported the deadly blast on Tuesday. The attack came on the third day of what the Taliban has called its spring offensive. Other explosions throughout the country killed nine civilians and a police commander.
In past years, spring has marked a significant upsurge in fighting between the Taliban and Nato forces with their local allies.
The insurgents warned they would infiltrate enemy ranks to conduct “insider attacks” and target military and diplomatic sites with suicide bombers.
This fighting season is a key test, as the international coalition is scheduled to hand over security responsibilities to Afghan forces next year.